There are 235 unlabeled trees on 11 vertices The set of Graham sequences of depth 3 has size 114. The sequences are {[11, 10, 9, 8], [11, 10, 10, 11], [11, 10, 10, 12], [11, 10, 10, 13], [11, 10, 11, 14], [11, 10, 11, 15], [11, 10, 11, 16], [11, 10, 11, 17], [11, 10, 11, 18], [11, 10, 11, 19], [11, 10, 12, 18], [11, 10, 12, 19], [11, 10, 12, 20], [11, 10, 12, 21], [11, 10, 12, 22], [11, 10, 12, 23], [11, 10, 12, 24], [11, 10, 12, 26], [11, 10, 13, 23], [11, 10, 13, 24], [11, 10, 13, 25], [11, 10, 13, 26], [11, 10, 13, 27], [11, 10, 13, 28], [11, 10, 13, 29], [11, 10, 13, 30], [11, 10, 13, 31], [11, 10, 13, 32], [11, 10, 14, 27], [11, 10, 14, 28], [11, 10, 14, 29], [11, 10, 14, 30], [11, 10, 14, 31], [11, 10, 14, 32], [11, 10, 14, 33], [11, 10, 14, 34], [11, 10, 14, 35], [11, 10, 14, 36], [11, 10, 15, 32], [11, 10, 15, 34], [11, 10, 15, 35], [11, 10, 15, 36], [11, 10, 15, 37], [11, 10, 15, 38], [11, 10, 15, 39], [11, 10, 15, 40], [11, 10, 15, 41], [11, 10, 15, 42], [11, 10, 15, 44], [11, 10, 15, 47], [11, 10, 15, 50], [11, 10, 16, 38], [11, 10, 16, 39], [11, 10, 16, 41], [11, 10, 16, 42], [11, 10, 16, 43], [11, 10, 16, 44], [11, 10, 16, 45], [11, 10, 16, 46], [11, 10, 16, 47], [11, 10, 16, 48], [11, 10, 16, 49], [11, 10, 16, 50], [11, 10, 16, 51], [11, 10, 16, 53], [11, 10, 17, 46], [11, 10, 17, 48], [11, 10, 17, 50], [11, 10, 17, 52], [11, 10, 17, 54], [11, 10, 17, 56], [11, 10, 18, 50], [11, 10, 18, 52], [11, 10, 18, 53], [11, 10, 18, 54], [11, 10, 18, 58], [11, 10, 18, 59], [11, 10, 18, 60], [11, 10, 18, 61], [11, 10, 18, 62], [11, 10, 19, 59], [11, 10, 19, 63], [11, 10, 19, 65], [11, 10, 19, 68], [11, 10, 19, 72], [11, 10, 19, 76], [11, 10, 19, 80], [11, 10, 20, 71], [11, 10, 20, 72], [11, 10, 20, 75], [11, 10, 20, 76], [11, 10, 20, 77], [11, 10, 20, 79], [11, 10, 20, 80], [11, 10, 20, 83], [11, 10, 21, 68], [11, 10, 21, 80], [11, 10, 21, 86], [11, 10, 22, 80], [11, 10, 22, 90], [11, 10, 22, 92], [11, 10, 24, 113], [11, 10, 24, 118], [11, 10, 24, 123], [11, 10, 25, 110], [11, 10, 25, 116], [11, 10, 25, 122], [11, 10, 25, 126], [11, 10, 27, 135], [11, 10, 30, 176], [11, 10, 30, 182], [11, 10, 31, 185], [11, 10, 37, 260], [11, 10, 45, 360]} Since there are not enough let's try depth 4 The set of Graham sequences of depth 4 has size 215. The sequences are {[11, 10, 9, 8, 7], [11, 10, 10, 11, 15], [11, 10, 10, 12, 20], [11, 10, 10, 12, 21], [11, 10, 10, 13, 26], [11, 10, 10, 13, 27], [11, 10, 10, 13, 28], [11, 10, 11, 14, 23], [11, 10, 11, 15, 28], [11, 10, 11, 15, 29], [11, 10, 11, 15, 30], [11, 10, 11, 16, 33], [11, 10, 11, 16, 34], [11, 10, 11, 16, 35], [11, 10, 11, 16, 36], [11, 10, 11, 16, 37], [11, 10, 11, 16, 38], [11, 10, 11, 17, 39], [11, 10, 11, 17, 41], [11, 10, 11, 17, 44], [11, 10, 11, 17, 45], [11, 10, 11, 17, 46], [11, 10, 11, 18, 46], [11, 10, 11, 18, 51], [11, 10, 11, 18, 52], [11, 10, 11, 19, 58], [11, 10, 12, 18, 38], [11, 10, 12, 19, 44], [11, 10, 12, 19, 45], [11, 10, 12, 19, 46], [11, 10, 12, 20, 51], [11, 10, 12, 20, 52], [11, 10, 12, 20, 53], [11, 10, 12, 20, 54], [11, 10, 12, 20, 55], [11, 10, 12, 20, 58], [11, 10, 12, 21, 58], [11, 10, 12, 21, 59], [11, 10, 12, 21, 60], [11, 10, 12, 21, 63], [11, 10, 12, 21, 65], [11, 10, 12, 22, 69], [11, 10, 12, 22, 70], [11, 10, 12, 22, 71], [11, 10, 12, 22, 73], [11, 10, 12, 22, 75], [11, 10, 12, 23, 75], [11, 10, 12, 23, 76], [11, 10, 12, 23, 77], [11, 10, 12, 24, 89], [11, 10, 12, 24, 91], [11, 10, 12, 24, 93], [11, 10, 12, 26, 106], [11, 10, 12, 26, 108], [11, 10, 13, 23, 66], [11, 10, 13, 24, 70], [11, 10, 13, 24, 71], [11, 10, 13, 24, 72], [11, 10, 13, 24, 74], [11, 10, 13, 25, 77], [11, 10, 13, 25, 80], [11, 10, 13, 25, 81], [11, 10, 13, 25, 83], [11, 10, 13, 25, 85], [11, 10, 13, 26, 86], [11, 10, 13, 26, 87], [11, 10, 13, 26, 89], [11, 10, 13, 26, 90], [11, 10, 13, 26, 91], [11, 10, 13, 26, 96], [11, 10, 13, 27, 94], [11, 10, 13, 27, 97], [11, 10, 13, 27, 101], [11, 10, 13, 27, 104], [11, 10, 13, 27, 105], [11, 10, 13, 27, 106], [11, 10, 13, 28, 104], [11, 10, 13, 28, 112], [11, 10, 13, 28, 113], [11, 10, 13, 28, 114], [11, 10, 13, 29, 116], [11, 10, 13, 29, 120], [11, 10, 13, 29, 121], [11, 10, 13, 29, 123], [11, 10, 13, 29, 125], [11, 10, 13, 30, 129], [11, 10, 13, 30, 130], [11, 10, 13, 31, 136], [11, 10, 13, 31, 141], [11, 10, 13, 32, 146], [11, 10, 14, 27, 83], [11, 10, 14, 28, 89], [11, 10, 14, 28, 95], [11, 10, 14, 29, 97], [11, 10, 14, 29, 98], [11, 10, 14, 29, 104], [11, 10, 14, 30, 106], [11, 10, 14, 30, 110], [11, 10, 14, 30, 113], [11, 10, 14, 30, 114], [11, 10, 14, 31, 121], [11, 10, 14, 31, 122], [11, 10, 14, 31, 123], [11, 10, 14, 31, 125], [11, 10, 14, 32, 128], [11, 10, 14, 32, 130], [11, 10, 14, 32, 133], [11, 10, 14, 33, 137], [11, 10, 14, 33, 140], [11, 10, 14, 33, 146], [11, 10, 14, 34, 148], [11, 10, 14, 34, 152], [11, 10, 14, 34, 153], [11, 10, 14, 34, 158], [11, 10, 14, 35, 163], [11, 10, 14, 36, 175], [11, 10, 15, 32, 109], [11, 10, 15, 34, 124], [11, 10, 15, 34, 130], [11, 10, 15, 35, 140], [11, 10, 15, 35, 146], [11, 10, 15, 36, 143], [11, 10, 15, 36, 144], [11, 10, 15, 37, 165], [11, 10, 15, 38, 184], [11, 10, 15, 38, 187], [11, 10, 15, 39, 192], [11, 10, 15, 40, 201], [11, 10, 15, 40, 202], [11, 10, 15, 41, 217], [11, 10, 15, 41, 220], [11, 10, 15, 42, 217], [11, 10, 15, 42, 219], [11, 10, 15, 44, 248], [11, 10, 15, 44, 251], [11, 10, 15, 47, 280], [11, 10, 15, 50, 310], [11, 10, 16, 38, 149], [11, 10, 16, 39, 161], [11, 10, 16, 41, 185], [11, 10, 16, 41, 194], [11, 10, 16, 41, 195], [11, 10, 16, 42, 191], [11, 10, 16, 42, 200], [11, 10, 16, 42, 204], [11, 10, 16, 43, 209], [11, 10, 16, 44, 224], [11, 10, 16, 44, 225], [11, 10, 16, 44, 231], [11, 10, 16, 45, 233], [11, 10, 16, 45, 234], [11, 10, 16, 45, 236], [11, 10, 16, 45, 245], [11, 10, 16, 46, 254], [11, 10, 16, 47, 259], [11, 10, 16, 47, 270], [11, 10, 16, 48, 276], [11, 10, 16, 48, 278], [11, 10, 16, 49, 284], [11, 10, 16, 50, 302], [11, 10, 16, 51, 307], [11, 10, 16, 53, 332], [11, 10, 17, 46, 221], [11, 10, 17, 48, 254], [11, 10, 17, 50, 271], [11, 10, 17, 50, 275], [11, 10, 17, 50, 281], [11, 10, 17, 52, 296], [11, 10, 17, 54, 329], [11, 10, 17, 56, 354], [11, 10, 18, 50, 238], [11, 10, 18, 52, 259], [11, 10, 18, 53, 274], [11, 10, 18, 54, 297], [11, 10, 18, 58, 358], [11, 10, 18, 59, 373], [11, 10, 18, 60, 375], [11, 10, 18, 61, 388], [11, 10, 18, 62, 403], [11, 10, 19, 59, 326], [11, 10, 19, 63, 392], [11, 10, 19, 65, 425], [11, 10, 19, 68, 477], [11, 10, 19, 72, 527], [11, 10, 19, 72, 531], [11, 10, 19, 76, 578], [11, 10, 19, 80, 626], [11, 10, 20, 71, 485], [11, 10, 20, 72, 494], [11, 10, 20, 75, 539], [11, 10, 20, 76, 560], [11, 10, 20, 77, 569], [11, 10, 20, 79, 605], [11, 10, 20, 80, 610], [11, 10, 20, 83, 653], [11, 10, 21, 68, 376], [11, 10, 21, 80, 574], [11, 10, 21, 80, 581], [11, 10, 21, 86, 680], [11, 10, 22, 80, 536], [11, 10, 22, 90, 701], [11, 10, 22, 92, 734], [11, 10, 24, 113, 1027], [11, 10, 24, 118, 1102], [11, 10, 24, 123, 1173], [11, 10, 25, 110, 920], [11, 10, 25, 116, 1040], [11, 10, 25, 122, 1139], [11, 10, 25, 126, 1205], [11, 10, 27, 135, 1296], [11, 10, 30, 176, 1960], [11, 10, 30, 182, 2059], [11, 10, 31, 185, 2096], [11, 10, 37, 260, 3416], [11, 10, 45, 360, 5400]} Since there are not enough let's try depth 5 The set of Graham sequences of depth 5 has size . The sequences are #___________________________________________________________________________ There are 551 unlabeled trees on 12 vertices The set of Graham sequences of depth 3 has size 188. The sequences are {[12, 11, 10, 9], [12, 11, 11, 12], [12, 11, 11, 13], [12, 11, 11, 14], [12, 11, 12, 15], [12, 11, 12, 16], [12, 11, 12, 17], [12, 11, 12, 18], [12, 11, 12, 19], [12, 11, 12, 20], [12, 11, 13, 19], [12, 11, 13, 20], [12, 11, 13, 21], [12, 11, 13, 22], [12, 11, 13, 23], [12, 11, 13, 24], [12, 11, 13, 25], [12, 11, 13, 27], [12, 11, 14, 24], [12, 11, 14, 25], [12, 11, 14, 26], [12, 11, 14, 27], [12, 11, 14, 28], [12, 11, 14, 29], [12, 11, 14, 30], [12, 11, 14, 31], [12, 11, 14, 32], [12, 11, 14, 33], [12, 11, 14, 34], [12, 11, 15, 28], [12, 11, 15, 29], [12, 11, 15, 30], [12, 11, 15, 31], [12, 11, 15, 32], [12, 11, 15, 33], [12, 11, 15, 34], [12, 11, 15, 35], [12, 11, 15, 36], [12, 11, 15, 37], [12, 11, 15, 38], [12, 11, 16, 33], [12, 11, 16, 34], [12, 11, 16, 35], [12, 11, 16, 36], [12, 11, 16, 37], [12, 11, 16, 38], [12, 11, 16, 39], [12, 11, 16, 40], [12, 11, 16, 41], [12, 11, 16, 42], [12, 11, 16, 43], [12, 11, 16, 45], [12, 11, 16, 48], [12, 11, 16, 51], [12, 11, 17, 37], [12, 11, 17, 38], [12, 11, 17, 39], [12, 11, 17, 40], [12, 11, 17, 41], [12, 11, 17, 42], [12, 11, 17, 43], [12, 11, 17, 44], [12, 11, 17, 45], [12, 11, 17, 46], [12, 11, 17, 47], [12, 11, 17, 48], [12, 11, 17, 49], [12, 11, 17, 50], [12, 11, 17, 51], [12, 11, 17, 52], [12, 11, 17, 53], [12, 11, 17, 54], [12, 11, 17, 55], [12, 11, 17, 57], [12, 11, 18, 46], [12, 11, 18, 47], [12, 11, 18, 48], [12, 11, 18, 49], [12, 11, 18, 50], [12, 11, 18, 51], [12, 11, 18, 52], [12, 11, 18, 53], [12, 11, 18, 54], [12, 11, 18, 55], [12, 11, 18, 56], [12, 11, 18, 57], [12, 11, 18, 58], [12, 11, 18, 60], [12, 11, 19, 51], [12, 11, 19, 53], [12, 11, 19, 54], [12, 11, 19, 55], [12, 11, 19, 56], [12, 11, 19, 57], [12, 11, 19, 59], [12, 11, 19, 60], [12, 11, 19, 61], [12, 11, 19, 62], [12, 11, 19, 63], [12, 11, 19, 64], [12, 11, 19, 65], [12, 11, 19, 66], [12, 11, 20, 57], [12, 11, 20, 58], [12, 11, 20, 60], [12, 11, 20, 61], [12, 11, 20, 62], [12, 11, 20, 63], [12, 11, 20, 65], [12, 11, 20, 66], [12, 11, 20, 67], [12, 11, 20, 68], [12, 11, 20, 69], [12, 11, 20, 73], [12, 11, 20, 77], [12, 11, 20, 81], [12, 11, 20, 85], [12, 11, 21, 72], [12, 11, 21, 73], [12, 11, 21, 74], [12, 11, 21, 76], [12, 11, 21, 77], [12, 11, 21, 78], [12, 11, 21, 80], [12, 11, 21, 81], [12, 11, 21, 82], [12, 11, 21, 84], [12, 11, 21, 85], [12, 11, 21, 88], [12, 11, 22, 69], [12, 11, 22, 72], [12, 11, 22, 75], [12, 11, 22, 77], [12, 11, 22, 78], [12, 11, 22, 80], [12, 11, 22, 81], [12, 11, 22, 82], [12, 11, 22, 83], [12, 11, 22, 84], [12, 11, 22, 85], [12, 11, 22, 88], [12, 11, 22, 91], [12, 11, 23, 79], [12, 11, 23, 81], [12, 11, 23, 83], [12, 11, 23, 85], [12, 11, 23, 87], [12, 11, 23, 91], [12, 11, 23, 93], [12, 11, 23, 95], [12, 11, 23, 97], [12, 11, 24, 91], [12, 11, 24, 96], [12, 11, 24, 100], [12, 11, 25, 114], [12, 11, 25, 119], [12, 11, 25, 124], [12, 11, 25, 129], [12, 11, 26, 99], [12, 11, 26, 114], [12, 11, 26, 115], [12, 11, 26, 117], [12, 11, 26, 118], [12, 11, 26, 122], [12, 11, 26, 123], [12, 11, 26, 124], [12, 11, 26, 127], [12, 11, 26, 128], [12, 11, 26, 132], [12, 11, 27, 127], [12, 11, 27, 135], [12, 11, 28, 126], [12, 11, 28, 138], [12, 11, 28, 141], [12, 11, 30, 145], [12, 11, 31, 159], [12, 11, 31, 177], [12, 11, 31, 183], [12, 11, 31, 189], [12, 11, 32, 180], [12, 11, 32, 187], [12, 11, 32, 192], [12, 11, 34, 201], [12, 11, 38, 261], [12, 11, 38, 268], [12, 11, 39, 271], [12, 11, 46, 369], [12, 11, 55, 495]} Since there are not enough let's try depth 4 The set of Graham sequences of depth 4 has size 465. The sequences are {[12, 11, 10, 9, 8], [12, 11, 11, 12, 16], [12, 11, 11, 13, 21], [12, 11, 11, 13, 22], [12, 11, 11, 14, 27], [12, 11, 11, 14, 28], [12, 11, 11, 14, 29], [12, 11, 12, 15, 24], [12, 11, 12, 16, 29], [12, 11, 12, 16, 30], [12, 11, 12, 16, 31], [12, 11, 12, 17, 34], [12, 11, 12, 17, 35], [12, 11, 12, 17, 36], [12, 11, 12, 17, 37], [12, 11, 12, 17, 38], [12, 11, 12, 17, 39], [12, 11, 12, 18, 40], [12, 11, 12, 18, 41], [12, 11, 12, 18, 42], [12, 11, 12, 18, 43], [12, 11, 12, 18, 45], [12, 11, 12, 18, 46], [12, 11, 12, 18, 47], [12, 11, 12, 19, 46], [12, 11, 12, 19, 48], [12, 11, 12, 19, 52], [12, 11, 12, 19, 53], [12, 11, 12, 19, 54], [12, 11, 12, 20, 59], [12, 11, 12, 20, 60], [12, 11, 13, 19, 38], [12, 11, 13, 19, 39], [12, 11, 13, 20, 44], [12, 11, 13, 20, 45], [12, 11, 13, 20, 46], [12, 11, 13, 20, 47], [12, 11, 13, 21, 50], [12, 11, 13, 21, 51], [12, 11, 13, 21, 52], [12, 11, 13, 21, 53], [12, 11, 13, 21, 54], [12, 11, 13, 21, 55], [12, 11, 13, 21, 56], [12, 11, 13, 21, 59], [12, 11, 13, 22, 58], [12, 11, 13, 22, 59], [12, 11, 13, 22, 60], [12, 11, 13, 22, 61], [12, 11, 13, 22, 62], [12, 11, 13, 22, 64], [12, 11, 13, 22, 66], [12, 11, 13, 23, 65], [12, 11, 13, 23, 66], [12, 11, 13, 23, 68], [12, 11, 13, 23, 70], [12, 11, 13, 23, 71], [12, 11, 13, 23, 72], [12, 11, 13, 23, 73], [12, 11, 13, 23, 74], [12, 11, 13, 23, 76], [12, 11, 13, 24, 77], [12, 11, 13, 24, 78], [12, 11, 13, 24, 79], [12, 11, 13, 25, 83], [12, 11, 13, 25, 84], [12, 11, 13, 25, 90], [12, 11, 13, 25, 92], [12, 11, 13, 25, 94], [12, 11, 13, 27, 107], [12, 11, 13, 27, 109], [12, 11, 13, 27, 111], [12, 11, 14, 24, 63], [12, 11, 14, 24, 64], [12, 11, 14, 24, 65], [12, 11, 14, 24, 67], [12, 11, 14, 25, 70], [12, 11, 14, 25, 72], [12, 11, 14, 25, 73], [12, 11, 14, 25, 74], [12, 11, 14, 25, 75], [12, 11, 14, 26, 77], [12, 11, 14, 26, 78], [12, 11, 14, 26, 79], [12, 11, 14, 26, 80], [12, 11, 14, 26, 81], [12, 11, 14, 26, 82], [12, 11, 14, 26, 84], [12, 11, 14, 26, 86], [12, 11, 14, 27, 87], [12, 11, 14, 27, 88], [12, 11, 14, 27, 89], [12, 11, 14, 27, 90], [12, 11, 14, 27, 91], [12, 11, 14, 27, 92], [12, 11, 14, 27, 93], [12, 11, 14, 27, 97], [12, 11, 14, 28, 93], [12, 11, 14, 28, 94], [12, 11, 14, 28, 95], [12, 11, 14, 28, 96], [12, 11, 14, 28, 97], [12, 11, 14, 28, 98], [12, 11, 14, 28, 99], [12, 11, 14, 28, 100], [12, 11, 14, 28, 102], [12, 11, 14, 28, 104], [12, 11, 14, 28, 105], [12, 11, 14, 28, 106], [12, 11, 14, 28, 107], [12, 11, 14, 29, 103], [12, 11, 14, 29, 106], [12, 11, 14, 29, 107], [12, 11, 14, 29, 113], [12, 11, 14, 29, 114], [12, 11, 14, 29, 115], [12, 11, 14, 30, 111], [12, 11, 14, 30, 115], [12, 11, 14, 30, 119], [12, 11, 14, 30, 121], [12, 11, 14, 30, 122], [12, 11, 14, 30, 123], [12, 11, 14, 30, 124], [12, 11, 14, 30, 126], [12, 11, 14, 31, 122], [12, 11, 14, 31, 130], [12, 11, 14, 31, 131], [12, 11, 14, 31, 132], [12, 11, 14, 31, 133], [12, 11, 14, 32, 138], [12, 11, 14, 32, 139], [12, 11, 14, 32, 142], [12, 11, 14, 32, 144], [12, 11, 14, 33, 148], [12, 11, 14, 33, 149], [12, 11, 14, 34, 155], [12, 11, 15, 28, 82], [12, 11, 15, 28, 83], [12, 11, 15, 29, 89], [12, 11, 15, 29, 90], [12, 11, 15, 29, 94], [12, 11, 15, 30, 96], [12, 11, 15, 30, 97], [12, 11, 15, 30, 99], [12, 11, 15, 30, 100], [12, 11, 15, 30, 101], [12, 11, 15, 30, 105], [12, 11, 15, 31, 105], [12, 11, 15, 31, 107], [12, 11, 15, 31, 109], [12, 11, 15, 31, 110], [12, 11, 15, 31, 111], [12, 11, 15, 31, 112], [12, 11, 15, 31, 113], [12, 11, 15, 31, 115], [12, 11, 15, 32, 113], [12, 11, 15, 32, 114], [12, 11, 15, 32, 117], [12, 11, 15, 32, 119], [12, 11, 15, 32, 120], [12, 11, 15, 32, 121], [12, 11, 15, 32, 122], [12, 11, 15, 32, 123], [12, 11, 15, 32, 124], [12, 11, 15, 32, 125], [12, 11, 15, 32, 126], [12, 11, 15, 33, 123], [12, 11, 15, 33, 127], [12, 11, 15, 33, 128], [12, 11, 15, 33, 129], [12, 11, 15, 33, 130], [12, 11, 15, 33, 132], [12, 11, 15, 33, 134], [12, 11, 15, 33, 136], [12, 11, 15, 34, 138], [12, 11, 15, 34, 139], [12, 11, 15, 34, 140], [12, 11, 15, 34, 141], [12, 11, 15, 34, 142], [12, 11, 15, 34, 143], [12, 11, 15, 34, 147], [12, 11, 15, 35, 145], [12, 11, 15, 35, 147], [12, 11, 15, 35, 151], [12, 11, 15, 35, 152], [12, 11, 15, 35, 154], [12, 11, 15, 35, 155], [12, 11, 15, 35, 159], [12, 11, 15, 36, 155], [12, 11, 15, 36, 158], [12, 11, 15, 36, 161], [12, 11, 15, 36, 165], [12, 11, 15, 36, 166], [12, 11, 15, 37, 167], [12, 11, 15, 37, 171], [12, 11, 15, 37, 172], [12, 11, 15, 37, 178], [12, 11, 15, 38, 183], [12, 11, 16, 33, 110], [12, 11, 16, 34, 117], [12, 11, 16, 34, 119], [12, 11, 16, 35, 125], [12, 11, 16, 35, 127], [12, 11, 16, 35, 129], [12, 11, 16, 35, 131], [12, 11, 16, 35, 132], [12, 11, 16, 35, 135], [12, 11, 16, 36, 140], [12, 11, 16, 36, 144], [12, 11, 16, 37, 140], [12, 11, 16, 37, 141], [12, 11, 16, 37, 146], [12, 11, 16, 37, 147], [12, 11, 16, 37, 149], [12, 11, 16, 37, 150], [12, 11, 16, 37, 153], [12, 11, 16, 37, 156], [12, 11, 16, 38, 157], [12, 11, 16, 38, 163], [12, 11, 16, 38, 169], [12, 11, 16, 39, 160], [12, 11, 16, 39, 162], [12, 11, 16, 39, 172], [12, 11, 16, 39, 173], [12, 11, 16, 39, 175], [12, 11, 16, 39, 185], [12, 11, 16, 39, 188], [12, 11, 16, 40, 184], [12, 11, 16, 41, 200], [12, 11, 16, 41, 202], [12, 11, 16, 41, 203], [12, 11, 16, 41, 204], [12, 11, 16, 41, 205], [12, 11, 16, 42, 213], [12, 11, 16, 42, 218], [12, 11, 16, 42, 221], [12, 11, 16, 43, 220], [12, 11, 16, 43, 222], [12, 11, 16, 45, 236], [12, 11, 16, 45, 237], [12, 11, 16, 45, 249], [12, 11, 16, 45, 252], [12, 11, 16, 45, 255], [12, 11, 16, 48, 281], [12, 11, 16, 48, 284], [12, 11, 16, 51, 314], [12, 11, 17, 37, 128], [12, 11, 17, 38, 141], [12, 11, 17, 39, 148], [12, 11, 17, 40, 158], [12, 11, 17, 41, 165], [12, 11, 17, 41, 166], [12, 11, 17, 41, 169], [12, 11, 17, 42, 177], [12, 11, 17, 42, 179], [12, 11, 17, 42, 187], [12, 11, 17, 42, 193], [12, 11, 17, 42, 196], [12, 11, 17, 43, 194], [12, 11, 17, 43, 200], [12, 11, 17, 43, 201], [12, 11, 17, 43, 202], [12, 11, 17, 43, 205], [12, 11, 17, 44, 202], [12, 11, 17, 44, 207], [12, 11, 17, 44, 211], [12, 11, 17, 44, 212], [12, 11, 17, 44, 213], [12, 11, 17, 45, 208], [12, 11, 17, 45, 209], [12, 11, 17, 45, 226], [12, 11, 17, 45, 229], [12, 11, 17, 45, 232], [12, 11, 17, 46, 231], [12, 11, 17, 46, 233], [12, 11, 17, 46, 235], [12, 11, 17, 46, 237], [12, 11, 17, 46, 239], [12, 11, 17, 46, 246], [12, 11, 17, 47, 240], [12, 11, 17, 47, 242], [12, 11, 17, 47, 244], [12, 11, 17, 47, 255], [12, 11, 17, 47, 256], [12, 11, 17, 48, 253], [12, 11, 17, 48, 254], [12, 11, 17, 48, 257], [12, 11, 17, 48, 263], [12, 11, 17, 48, 271], [12, 11, 17, 49, 265], [12, 11, 17, 49, 277], [12, 11, 17, 49, 279], [12, 11, 17, 49, 280], [12, 11, 17, 50, 286], [12, 11, 17, 50, 288], [12, 11, 17, 51, 292], [12, 11, 17, 51, 303], [12, 11, 17, 51, 306], [12, 11, 17, 52, 309], [12, 11, 17, 52, 311], [12, 11, 17, 53, 317], [12, 11, 17, 54, 336], [12, 11, 17, 55, 341], [12, 11, 17, 57, 367], [12, 11, 18, 46, 200], [12, 11, 18, 46, 209], [12, 11, 18, 46, 214], [12, 11, 18, 47, 219], [12, 11, 18, 48, 226], [12, 11, 18, 48, 228], [12, 11, 18, 48, 229], [12, 11, 18, 48, 243], [12, 11, 18, 49, 245], [12, 11, 18, 49, 254], [12, 11, 18, 50, 252], [12, 11, 18, 50, 260], [12, 11, 18, 50, 264], [12, 11, 18, 51, 270], [12, 11, 18, 51, 273], [12, 11, 18, 51, 274], [12, 11, 18, 51, 277], [12, 11, 18, 51, 279], [12, 11, 18, 52, 279], [12, 11, 18, 52, 282], [12, 11, 18, 52, 286], [12, 11, 18, 52, 287], [12, 11, 18, 52, 290], [12, 11, 18, 53, 300], [12, 11, 18, 54, 303], [12, 11, 18, 54, 307], [12, 11, 18, 54, 314], [12, 11, 18, 55, 331], [12, 11, 18, 56, 329], [12, 11, 18, 56, 338], [12, 11, 18, 56, 339], [12, 11, 18, 57, 358], [12, 11, 18, 58, 363], [12, 11, 18, 60, 389], [12, 11, 19, 51, 239], [12, 11, 19, 51, 240], [12, 11, 19, 53, 254], [12, 11, 19, 53, 262], [12, 11, 19, 54, 269], [12, 11, 19, 54, 278], [12, 11, 19, 55, 276], [12, 11, 19, 55, 291], [12, 11, 19, 55, 299], [12, 11, 19, 56, 290], [12, 11, 19, 57, 306], [12, 11, 19, 57, 315], [12, 11, 19, 57, 318], [12, 11, 19, 59, 351], [12, 11, 19, 59, 359], [12, 11, 19, 60, 374], [12, 11, 19, 61, 378], [12, 11, 19, 62, 391], [12, 11, 19, 62, 392], [12, 11, 19, 63, 396], [12, 11, 19, 63, 407], [12, 11, 19, 63, 411], [12, 11, 19, 64, 408], [12, 11, 19, 65, 422], [12, 11, 19, 66, 438], [12, 11, 20, 57, 280], [12, 11, 20, 58, 293], [12, 11, 20, 58, 299], [12, 11, 20, 60, 328], [12, 11, 20, 61, 338], [12, 11, 20, 62, 343], [12, 11, 20, 62, 369], [12, 11, 20, 63, 358], [12, 11, 20, 63, 385], [12, 11, 20, 65, 400], [12, 11, 20, 66, 413], [12, 11, 20, 67, 425], [12, 11, 20, 67, 434], [12, 11, 20, 68, 444], [12, 11, 20, 69, 460], [12, 11, 20, 69, 478], [12, 11, 20, 73, 528], [12, 11, 20, 73, 532], [12, 11, 20, 77, 579], [12, 11, 20, 77, 583], [12, 11, 20, 81, 631], [12, 11, 20, 85, 680], [12, 11, 21, 72, 486], [12, 11, 21, 73, 491], [12, 11, 21, 73, 496], [12, 11, 21, 74, 501], [12, 11, 21, 76, 536], [12, 11, 21, 76, 544], [12, 11, 21, 77, 545], [12, 11, 21, 77, 561], [12, 11, 21, 78, 571], [12, 11, 21, 80, 591], [12, 11, 21, 80, 606], [12, 11, 21, 81, 612], [12, 11, 21, 81, 615], [12, 11, 21, 82, 621], [12, 11, 21, 84, 658], [12, 11, 21, 85, 663], [12, 11, 21, 88, 707], [12, 11, 22, 69, 368], [12, 11, 22, 72, 407], [12, 11, 22, 75, 474], [12, 11, 22, 77, 513], [12, 11, 22, 78, 531], [12, 11, 22, 80, 570], [12, 11, 22, 81, 578], [12, 11, 22, 82, 588], [12, 11, 22, 82, 593], [12, 11, 22, 83, 618], [12, 11, 22, 84, 608], [12, 11, 22, 84, 609], [12, 11, 22, 85, 633], [12, 11, 22, 88, 690], [12, 11, 22, 91, 734], [12, 11, 23, 79, 479], [12, 11, 23, 81, 529], [12, 11, 23, 83, 552], [12, 11, 23, 85, 587], [12, 11, 23, 87, 631], [12, 11, 23, 91, 704], [12, 11, 23, 93, 722], [12, 11, 23, 93, 739], [12, 11, 23, 95, 754], [12, 11, 23, 97, 788], [12, 11, 24, 91, 644], [12, 11, 24, 96, 739], [12, 11, 24, 100, 815], [12, 11, 25, 114, 1028], [12, 11, 25, 119, 1103], [12, 11, 25, 119, 1108], [12, 11, 25, 124, 1179], [12, 11, 25, 129, 1251], [12, 11, 26, 99, 670], [12, 11, 26, 114, 955], [12, 11, 26, 115, 974], [12, 11, 26, 117, 1036], [12, 11, 26, 118, 1046], [12, 11, 26, 122, 1116], [12, 11, 26, 123, 1141], [12, 11, 26, 124, 1151], [12, 11, 26, 127, 1211], [12, 11, 26, 128, 1216], [12, 11, 26, 132, 1283], [12, 11, 27, 127, 1163], [12, 11, 27, 135, 1315], [12, 11, 28, 126, 1089], [12, 11, 28, 138, 1317], [12, 11, 28, 141, 1374], [12, 11, 30, 145, 1340], [12, 11, 31, 159, 1575], [12, 11, 31, 177, 1961], [12, 11, 31, 183, 2066], [12, 11, 31, 189, 2166], [12, 11, 32, 180, 1975], [12, 11, 32, 187, 2108], [12, 11, 32, 192, 2203], [12, 11, 34, 201, 2304], [12, 11, 38, 261, 3424], [12, 11, 38, 268, 3557], [12, 11, 39, 271, 3599], [12, 11, 46, 369, 5580], [12, 11, 55, 495, 8415]} There are 1301 unlabeled trees on 13 vertices The set of Graham sequences of depth 3 has size 300. The sequences are {[13, 12, 11, 10], [13, 12, 12, 13], [13, 12, 12, 14], [13, 12, 12, 15], [13, 12, 13, 16], [13, 12, 13, 17], [13, 12, 13, 18], [13, 12, 13, 19], [13, 12, 13, 20], [13, 12, 13, 21], [13, 12, 14, 20], [13, 12, 14, 21], [13, 12, 14, 22], [13, 12, 14, 23], [13, 12, 14, 24], [13, 12, 14, 25], [13, 12, 14, 26], [13, 12, 14, 27], [13, 12, 14, 28], [13, 12, 15, 24], [13, 12, 15, 25], [13, 12, 15, 26], [13, 12, 15, 27], [13, 12, 15, 28], [13, 12, 15, 29], [13, 12, 15, 30], [13, 12, 15, 31], [13, 12, 15, 32], [13, 12, 15, 33], [13, 12, 15, 34], [13, 12, 15, 35], [13, 12, 16, 29], [13, 12, 16, 30], [13, 12, 16, 31], [13, 12, 16, 32], [13, 12, 16, 33], [13, 12, 16, 34], [13, 12, 16, 35], [13, 12, 16, 36], [13, 12, 16, 37], [13, 12, 16, 38], [13, 12, 16, 39], [13, 12, 16, 40], [13, 12, 17, 34], [13, 12, 17, 35], [13, 12, 17, 36], [13, 12, 17, 37], [13, 12, 17, 38], [13, 12, 17, 39], [13, 12, 17, 40], [13, 12, 17, 41], [13, 12, 17, 42], [13, 12, 17, 43], [13, 12, 17, 44], [13, 12, 17, 46], [13, 12, 17, 48], [13, 12, 17, 49], [13, 12, 17, 52], [13, 12, 18, 38], [13, 12, 18, 39], [13, 12, 18, 40], [13, 12, 18, 41], [13, 12, 18, 42], [13, 12, 18, 43], [13, 12, 18, 44], [13, 12, 18, 45], [13, 12, 18, 46], [13, 12, 18, 47], [13, 12, 18, 48], [13, 12, 18, 49], [13, 12, 18, 50], [13, 12, 18, 51], [13, 12, 18, 52], [13, 12, 18, 53], [13, 12, 18, 54], [13, 12, 18, 55], [13, 12, 18, 56], [13, 12, 18, 57], [13, 12, 18, 58], [13, 12, 18, 59], [13, 12, 19, 45], [13, 12, 19, 46], [13, 12, 19, 47], [13, 12, 19, 48], [13, 12, 19, 49], [13, 12, 19, 50], [13, 12, 19, 51], [13, 12, 19, 52], [13, 12, 19, 53], [13, 12, 19, 54], [13, 12, 19, 55], [13, 12, 19, 56], [13, 12, 19, 57], [13, 12, 19, 58], [13, 12, 19, 59], [13, 12, 19, 60], [13, 12, 19, 61], [13, 12, 19, 62], [13, 12, 19, 64], [13, 12, 20, 48], [13, 12, 20, 52], [13, 12, 20, 53], [13, 12, 20, 54], [13, 12, 20, 55], [13, 12, 20, 56], [13, 12, 20, 57], [13, 12, 20, 58], [13, 12, 20, 59], [13, 12, 20, 60], [13, 12, 20, 61], [13, 12, 20, 62], [13, 12, 20, 63], [13, 12, 20, 64], [13, 12, 20, 65], [13, 12, 20, 66], [13, 12, 20, 67], [13, 12, 20, 68], [13, 12, 20, 69], [13, 12, 20, 70], [13, 12, 21, 56], [13, 12, 21, 57], [13, 12, 21, 58], [13, 12, 21, 59], [13, 12, 21, 60], [13, 12, 21, 61], [13, 12, 21, 62], [13, 12, 21, 63], [13, 12, 21, 64], [13, 12, 21, 65], [13, 12, 21, 66], [13, 12, 21, 67], [13, 12, 21, 68], [13, 12, 21, 69], [13, 12, 21, 70], [13, 12, 21, 71], [13, 12, 21, 72], [13, 12, 21, 73], [13, 12, 21, 74], [13, 12, 21, 78], [13, 12, 21, 82], [13, 12, 21, 86], [13, 12, 21, 90], [13, 12, 22, 66], [13, 12, 22, 68], [13, 12, 22, 70], [13, 12, 22, 72], [13, 12, 22, 73], [13, 12, 22, 74], [13, 12, 22, 75], [13, 12, 22, 76], [13, 12, 22, 77], [13, 12, 22, 78], [13, 12, 22, 79], [13, 12, 22, 81], [13, 12, 22, 82], [13, 12, 22, 83], [13, 12, 22, 85], [13, 12, 22, 86], [13, 12, 22, 87], [13, 12, 22, 89], [13, 12, 22, 90], [13, 12, 22, 93], [13, 12, 23, 70], [13, 12, 23, 72], [13, 12, 23, 73], [13, 12, 23, 76], [13, 12, 23, 77], [13, 12, 23, 78], [13, 12, 23, 79], [13, 12, 23, 80], [13, 12, 23, 81], [13, 12, 23, 82], [13, 12, 23, 83], [13, 12, 23, 84], [13, 12, 23, 85], [13, 12, 23, 86], [13, 12, 23, 87], [13, 12, 23, 88], [13, 12, 23, 89], [13, 12, 23, 90], [13, 12, 23, 92], [13, 12, 23, 93], [13, 12, 23, 96], [13, 12, 24, 77], [13, 12, 24, 79], [13, 12, 24, 81], [13, 12, 24, 82], [13, 12, 24, 83], [13, 12, 24, 84], [13, 12, 24, 85], [13, 12, 24, 86], [13, 12, 24, 87], [13, 12, 24, 88], [13, 12, 24, 89], [13, 12, 24, 90], [13, 12, 24, 91], [13, 12, 24, 92], [13, 12, 24, 93], [13, 12, 24, 94], [13, 12, 24, 96], [13, 12, 24, 98], [13, 12, 24, 99], [13, 12, 24, 100], [13, 12, 24, 102], [13, 12, 25, 88], [13, 12, 25, 89], [13, 12, 25, 90], [13, 12, 25, 93], [13, 12, 25, 94], [13, 12, 25, 95], [13, 12, 25, 96], [13, 12, 25, 97], [13, 12, 25, 98], [13, 12, 25, 99], [13, 12, 25, 101], [13, 12, 25, 102], [13, 12, 25, 103], [13, 12, 25, 105], [13, 12, 26, 96], [13, 12, 26, 100], [13, 12, 26, 115], [13, 12, 26, 120], [13, 12, 26, 125], [13, 12, 26, 130], [13, 12, 26, 135], [13, 12, 27, 100], [13, 12, 27, 103], [13, 12, 27, 104], [13, 12, 27, 108], [13, 12, 27, 114], [13, 12, 27, 115], [13, 12, 27, 116], [13, 12, 27, 118], [13, 12, 27, 119], [13, 12, 27, 120], [13, 12, 27, 123], [13, 12, 27, 124], [13, 12, 27, 125], [13, 12, 27, 128], [13, 12, 27, 129], [13, 12, 27, 130], [13, 12, 27, 133], [13, 12, 27, 134], [13, 12, 27, 138], [13, 12, 28, 111], [13, 12, 28, 121], [13, 12, 28, 123], [13, 12, 28, 127], [13, 12, 28, 129], [13, 12, 28, 131], [13, 12, 28, 133], [13, 12, 28, 137], [13, 12, 28, 141], [13, 12, 29, 127], [13, 12, 29, 129], [13, 12, 29, 132], [13, 12, 29, 139], [13, 12, 29, 141], [13, 12, 29, 142], [13, 12, 29, 144], [13, 12, 29, 147], [13, 12, 30, 138], [13, 12, 30, 144], [13, 12, 30, 150], [13, 12, 31, 130], [13, 12, 31, 150], [13, 12, 32, 145], [13, 12, 32, 163], [13, 12, 32, 165], [13, 12, 32, 178], [13, 12, 32, 184], [13, 12, 32, 190], [13, 12, 32, 196], [13, 12, 33, 181], [13, 12, 33, 182], [13, 12, 33, 187], [13, 12, 33, 188], [13, 12, 33, 189], [13, 12, 33, 193], [13, 12, 33, 194], [13, 12, 33, 199], [13, 12, 34, 192], [13, 12, 34, 202], [13, 12, 35, 190], [13, 12, 35, 204], [13, 12, 35, 208], [13, 12, 36, 195], [13, 12, 38, 226], [13, 12, 39, 262], [13, 12, 39, 269], [13, 12, 39, 276], [13, 12, 40, 265], [13, 12, 40, 273], [13, 12, 40, 279], [13, 12, 42, 288], [13, 12, 47, 370], [13, 12, 47, 378], [13, 12, 48, 381], [13, 12, 56, 505], [13, 12, 66, 660]} Since there are not enough let's try depth 4 The set of Graham sequences of depth 4 has size 980. The sequences are {[13, 12, 11, 10, 9], [13, 12, 12, 13, 17], [13, 12, 12, 14, 22], [13, 12, 12, 14, 23], [13, 12, 12, 15, 28], [13, 12, 12, 15, 29], [13, 12, 12, 15, 30], [13, 12, 13, 16, 25], [13, 12, 13, 17, 30], [13, 12, 13, 17, 31], [13, 12, 13, 17, 32], [13, 12, 13, 18, 35], [13, 12, 13, 18, 36], [13, 12, 13, 18, 37], [13, 12, 13, 18, 38], [13, 12, 13, 18, 39], [13, 12, 13, 18, 40], [13, 12, 13, 19, 41], [13, 12, 13, 19, 42], [13, 12, 13, 19, 43], [13, 12, 13, 19, 44], [13, 12, 13, 19, 45], [13, 12, 13, 19, 46], [13, 12, 13, 19, 47], [13, 12, 13, 19, 48], [13, 12, 13, 20, 47], [13, 12, 13, 20, 48], [13, 12, 13, 20, 49], [13, 12, 13, 20, 50], [13, 12, 13, 20, 53], [13, 12, 13, 20, 54], [13, 12, 13, 20, 55], [13, 12, 13, 21, 60], [13, 12, 13, 21, 61], [13, 12, 13, 21, 62], [13, 12, 14, 20, 39], [13, 12, 14, 20, 40], [13, 12, 14, 21, 44], [13, 12, 14, 21, 45], [13, 12, 14, 21, 46], [13, 12, 14, 21, 47], [13, 12, 14, 21, 48], [13, 12, 14, 22, 50], [13, 12, 14, 22, 51], [13, 12, 14, 22, 52], [13, 12, 14, 22, 53], [13, 12, 14, 22, 54], [13, 12, 14, 22, 55], [13, 12, 14, 22, 56], [13, 12, 14, 22, 57], [13, 12, 14, 22, 60], [13, 12, 14, 23, 57], [13, 12, 14, 23, 58], [13, 12, 14, 23, 59], [13, 12, 14, 23, 60], [13, 12, 14, 23, 61], [13, 12, 14, 23, 62], [13, 12, 14, 23, 63], [13, 12, 14, 23, 64], [13, 12, 14, 23, 65], [13, 12, 14, 23, 67], [13, 12, 14, 24, 65], [13, 12, 14, 24, 66], [13, 12, 14, 24, 67], [13, 12, 14, 24, 68], [13, 12, 14, 24, 70], [13, 12, 14, 24, 71], [13, 12, 14, 24, 72], [13, 12, 14, 24, 73], [13, 12, 14, 24, 74], [13, 12, 14, 24, 75], [13, 12, 14, 24, 77], [13, 12, 14, 25, 73], [13, 12, 14, 25, 74], [13, 12, 14, 25, 78], [13, 12, 14, 25, 79], [13, 12, 14, 25, 80], [13, 12, 14, 25, 81], [13, 12, 14, 26, 85], [13, 12, 14, 26, 86], [13, 12, 14, 26, 91], [13, 12, 14, 26, 93], [13, 12, 14, 26, 95], [13, 12, 14, 27, 92], [13, 12, 14, 28, 108], [13, 12, 14, 28, 110], [13, 12, 14, 28, 112], [13, 12, 14, 28, 114], [13, 12, 15, 24, 56], [13, 12, 15, 24, 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663], [13, 12, 22, 86, 665], [13, 12, 22, 86, 668], [13, 12, 22, 87, 674], [13, 12, 22, 89, 712], [13, 12, 22, 90, 717], [13, 12, 22, 93, 762], [13, 12, 23, 70, 369], [13, 12, 23, 70, 372], [13, 12, 23, 72, 415], [13, 12, 23, 73, 399], [13, 12, 23, 73, 411], [13, 12, 23, 73, 432], [13, 12, 23, 76, 438], [13, 12, 23, 76, 439], [13, 12, 23, 77, 506], [13, 12, 23, 78, 492], [13, 12, 23, 78, 496], [13, 12, 23, 78, 510], [13, 12, 23, 79, 507], [13, 12, 23, 79, 520], [13, 12, 23, 79, 521], [13, 12, 23, 80, 557], [13, 12, 23, 81, 550], [13, 12, 23, 81, 570], [13, 12, 23, 82, 564], [13, 12, 23, 82, 567], [13, 12, 23, 82, 576], [13, 12, 23, 82, 579], [13, 12, 23, 82, 581], [13, 12, 23, 83, 590], [13, 12, 23, 83, 595], [13, 12, 23, 84, 596], [13, 12, 23, 84, 600], [13, 12, 23, 84, 615], [13, 12, 23, 85, 612], [13, 12, 23, 85, 613], [13, 12, 23, 85, 622], [13, 12, 23, 85, 624], [13, 12, 23, 85, 628], [13, 12, 23, 86, 638], [13, 12, 23, 87, 640], [13, 12, 23, 87, 645], [13, 12, 23, 88, 643], [13, 12, 23, 88, 645], [13, 12, 23, 88, 671], [13, 12, 23, 89, 692], [13, 12, 23, 90, 686], [13, 12, 23, 90, 700], [13, 12, 23, 90, 701], [13, 12, 23, 92, 739], [13, 12, 23, 93, 744], [13, 12, 23, 96, 789], [13, 12, 24, 77, 430], [13, 12, 24, 79, 461], [13, 12, 24, 81, 492], [13, 12, 24, 82, 530], [13, 12, 24, 83, 511], [13, 12, 24, 84, 545], [13, 12, 24, 84, 555], [13, 12, 24, 85, 590], [13, 12, 24, 86, 569], [13, 12, 24, 86, 580], [13, 12, 24, 86, 592], [13, 12, 24, 87, 608], [13, 12, 24, 87, 618], [13, 12, 24, 88, 603], [13, 12, 24, 89, 640], [13, 12, 24, 90, 639], [13, 12, 24, 91, 665], [13, 12, 24, 91, 667], [13, 12, 24, 92, 705], [13, 12, 24, 93, 713], [13, 12, 24, 94, 725], [13, 12, 24, 94, 740], [13, 12, 24, 96, 744], [13, 12, 24, 96, 757], [13, 12, 24, 96, 759], [13, 12, 24, 98, 775], [13, 12, 24, 98, 793], [13, 12, 24, 99, 816], [13, 12, 24, 100, 808], [13, 12, 24, 102, 843], [13, 12, 25, 88, 572], [13, 12, 25, 89, 586], [13, 12, 25, 90, 615], [13, 12, 25, 93, 657], [13, 12, 25, 93, 666], [13, 12, 25, 94, 661], [13, 12, 25, 95, 715], [13, 12, 25, 96, 696], [13, 12, 25, 97, 752], [13, 12, 25, 98, 747], [13, 12, 25, 99, 761], [13, 12, 25, 101, 792], [13, 12, 25, 102, 825], [13, 12, 25, 103, 835], [13, 12, 25, 105, 870], [13, 12, 26, 96, 652], [13, 12, 26, 100, 738], [13, 12, 26, 115, 1029], [13, 12, 26, 120, 1104], [13, 12, 26, 120, 1109], [13, 12, 26, 125, 1180], [13, 12, 26, 125, 1185], [13, 12, 26, 130, 1257], [13, 12, 26, 135, 1330], [13, 12, 27, 100, 659], [13, 12, 27, 103, 701], [13, 12, 27, 104, 721], [13, 12, 27, 108, 822], [13, 12, 27, 114, 951], [13, 12, 27, 115, 959], [13, 12, 27, 116, 979], [13, 12, 27, 118, 991], [13, 12, 27, 118, 1037], [13, 12, 27, 119, 1009], [13, 12, 27, 119, 1042], [13, 12, 27, 119, 1048], [13, 12, 27, 120, 1029], [13, 12, 27, 120, 1053], [13, 12, 27, 123, 1112], [13, 12, 27, 123, 1122], [13, 12, 27, 124, 1122], [13, 12, 27, 124, 1142], [13, 12, 27, 125, 1153], [13, 12, 27, 128, 1193], [13, 12, 27, 128, 1212], [13, 12, 27, 129, 1218], [13, 12, 27, 129, 1222], [13, 12, 27, 130, 1228], [13, 12, 27, 133, 1289], [13, 12, 27, 134, 1294], [13, 12, 27, 138, 1362], [13, 12, 28, 111, 798], [13, 12, 28, 121, 1013], [13, 12, 28, 123, 1056], [13, 12, 28, 123, 1065], [13, 12, 28, 127, 1151], [13, 12, 28, 129, 1170], [13, 12, 28, 129, 1176], [13, 12, 28, 131, 1225], [13, 12, 28, 133, 1240], [13, 12, 28, 137, 1326], [13, 12, 28, 141, 1394], [13, 12, 29, 127, 1080], [13, 12, 29, 129, 1105], [13, 12, 29, 132, 1165], [13, 12, 29, 139, 1320], [13, 12, 29, 141, 1339], [13, 12, 29, 142, 1380], [13, 12, 29, 144, 1395], [13, 12, 29, 147, 1453], [13, 12, 30, 138, 1227], [13, 12, 30, 144, 1356], [13, 12, 30, 150, 1485], [13, 12, 31, 130, 965], [13, 12, 31, 150, 1395], [13, 12, 32, 145, 1224], [13, 12, 32, 163, 1611], [13, 12, 32, 165, 1654], [13, 12, 32, 178, 1962], [13, 12, 32, 184, 2067], [13, 12, 32, 184, 2073], [13, 12, 32, 190, 2173], [13, 12, 32, 196, 2274], [13, 12, 33, 181, 1970], [13, 12, 33, 182, 1981], [13, 12, 33, 187, 2081], [13, 12, 33, 188, 2110], [13, 12, 33, 189, 2121], [13, 12, 33, 193, 2210], [13, 12, 33, 194, 2215], [13, 12, 33, 199, 2311], [13, 12, 34, 192, 2133], [13, 12, 34, 202, 2348], [13, 12, 35, 190, 2025], [13, 12, 35, 204, 2326], [13, 12, 35, 208, 2412], [13, 12, 36, 195, 2040], [13, 12, 38, 226, 2628], [13, 12, 39, 262, 3425], [13, 12, 39, 269, 3565], [13, 12, 39, 276, 3699], [13, 12, 40, 265, 3440], [13, 12, 40, 273, 3612], [13, 12, 40, 279, 3741], [13, 12, 42, 288, 3852], [13, 12, 47, 370, 5589], [13, 12, 47, 378, 5761], [13, 12, 48, 381, 5808], [13, 12, 56, 505, 8640], [13, 12, 66, 660, 12540]} There are 3159 unlabeled trees on 14 vertices The set of Graham sequences of depth 3 has size 462. The sequences are {[14, 13, 12, 11], [14, 13, 13, 14], [14, 13, 13, 15], [14, 13, 13, 16], [14, 13, 14, 17], [14, 13, 14, 18], [14, 13, 14, 19], [14, 13, 14, 20], [14, 13, 14, 21], [14, 13, 14, 22], [14, 13, 15, 21], [14, 13, 15, 22], [14, 13, 15, 23], [14, 13, 15, 24], [14, 13, 15, 25], [14, 13, 15, 26], [14, 13, 15, 27], [14, 13, 15, 28], [14, 13, 15, 29], [14, 13, 16, 25], [14, 13, 16, 26], [14, 13, 16, 27], [14, 13, 16, 28], [14, 13, 16, 29], [14, 13, 16, 30], [14, 13, 16, 31], [14, 13, 16, 32], [14, 13, 16, 33], [14, 13, 16, 34], [14, 13, 16, 35], [14, 13, 16, 36], [14, 13, 17, 30], [14, 13, 17, 31], [14, 13, 17, 32], [14, 13, 17, 33], [14, 13, 17, 34], [14, 13, 17, 35], [14, 13, 17, 36], [14, 13, 17, 37], [14, 13, 17, 38], [14, 13, 17, 39], [14, 13, 17, 40], [14, 13, 17, 41], [14, 13, 17, 42], [14, 13, 18, 34], [14, 13, 18, 35], [14, 13, 18, 36], [14, 13, 18, 37], [14, 13, 18, 38], [14, 13, 18, 39], [14, 13, 18, 40], [14, 13, 18, 41], [14, 13, 18, 42], [14, 13, 18, 43], [14, 13, 18, 44], [14, 13, 18, 45], [14, 13, 18, 46], [14, 13, 18, 47], [14, 13, 18, 49], [14, 13, 18, 50], [14, 13, 18, 51], [14, 13, 18, 53], [14, 13, 19, 39], [14, 13, 19, 40], [14, 13, 19, 41], [14, 13, 19, 42], [14, 13, 19, 43], [14, 13, 19, 44], [14, 13, 19, 45], [14, 13, 19, 46], [14, 13, 19, 47], [14, 13, 19, 48], [14, 13, 19, 49], [14, 13, 19, 50], [14, 13, 19, 51], [14, 13, 19, 52], [14, 13, 19, 53], [14, 13, 19, 54], [14, 13, 19, 55], [14, 13, 19, 56], [14, 13, 19, 57], [14, 13, 19, 58], [14, 13, 19, 59], [14, 13, 19, 60], [14, 13, 19, 61], [14, 13, 20, 44], [14, 13, 20, 45], [14, 13, 20, 46], [14, 13, 20, 47], [14, 13, 20, 48], [14, 13, 20, 49], [14, 13, 20, 50], [14, 13, 20, 51], [14, 13, 20, 52], [14, 13, 20, 53], [14, 13, 20, 54], [14, 13, 20, 55], [14, 13, 20, 56], [14, 13, 20, 57], [14, 13, 20, 58], [14, 13, 20, 59], [14, 13, 20, 60], [14, 13, 20, 61], [14, 13, 20, 62], [14, 13, 20, 63], [14, 13, 20, 64], [14, 13, 20, 65], [14, 13, 20, 66], [14, 13, 21, 49], [14, 13, 21, 51], [14, 13, 21, 53], [14, 13, 21, 54], [14, 13, 21, 55], [14, 13, 21, 56], [14, 13, 21, 57], [14, 13, 21, 58], [14, 13, 21, 59], [14, 13, 21, 60], [14, 13, 21, 61], [14, 13, 21, 62], [14, 13, 21, 63], [14, 13, 21, 64], [14, 13, 21, 65], [14, 13, 21, 66], [14, 13, 21, 67], [14, 13, 21, 68], [14, 13, 21, 69], [14, 13, 21, 70], [14, 13, 21, 71], [14, 13, 21, 72], [14, 13, 21, 73], [14, 13, 22, 56], [14, 13, 22, 57], [14, 13, 22, 58], [14, 13, 22, 59], [14, 13, 22, 60], [14, 13, 22, 61], [14, 13, 22, 62], [14, 13, 22, 63], [14, 13, 22, 64], [14, 13, 22, 65], [14, 13, 22, 66], [14, 13, 22, 67], [14, 13, 22, 68], [14, 13, 22, 69], [14, 13, 22, 70], [14, 13, 22, 71], [14, 13, 22, 72], [14, 13, 22, 73], [14, 13, 22, 74], [14, 13, 22, 75], [14, 13, 22, 76], [14, 13, 22, 77], [14, 13, 22, 79], [14, 13, 22, 83], [14, 13, 22, 87], [14, 13, 22, 91], [14, 13, 23, 64], [14, 13, 23, 65], [14, 13, 23, 66], [14, 13, 23, 67], [14, 13, 23, 68], [14, 13, 23, 69], [14, 13, 23, 70], [14, 13, 23, 71], [14, 13, 23, 72], [14, 13, 23, 73], [14, 13, 23, 74], [14, 13, 23, 75], [14, 13, 23, 76], [14, 13, 23, 77], [14, 13, 23, 78], [14, 13, 23, 79], [14, 13, 23, 80], [14, 13, 23, 82], [14, 13, 23, 83], [14, 13, 23, 84], [14, 13, 23, 86], [14, 13, 23, 87], [14, 13, 23, 88], [14, 13, 23, 90], [14, 13, 23, 91], [14, 13, 23, 92], [14, 13, 23, 94], [14, 13, 23, 95], [14, 13, 23, 98], [14, 13, 24, 67], [14, 13, 24, 68], [14, 13, 24, 71], [14, 13, 24, 73], [14, 13, 24, 74], [14, 13, 24, 75], [14, 13, 24, 76], [14, 13, 24, 77], [14, 13, 24, 78], [14, 13, 24, 79], [14, 13, 24, 80], [14, 13, 24, 81], [14, 13, 24, 82], [14, 13, 24, 83], [14, 13, 24, 84], [14, 13, 24, 85], [14, 13, 24, 86], [14, 13, 24, 87], [14, 13, 24, 88], [14, 13, 24, 89], [14, 13, 24, 90], [14, 13, 24, 91], [14, 13, 24, 92], [14, 13, 24, 93], [14, 13, 24, 94], [14, 13, 24, 95], [14, 13, 24, 97], [14, 13, 24, 98], [14, 13, 24, 101], [14, 13, 25, 75], [14, 13, 25, 77], [14, 13, 25, 78], [14, 13, 25, 79], [14, 13, 25, 80], [14, 13, 25, 81], [14, 13, 25, 82], [14, 13, 25, 83], [14, 13, 25, 84], [14, 13, 25, 85], [14, 13, 25, 86], [14, 13, 25, 87], [14, 13, 25, 89], [14, 13, 25, 90], [14, 13, 25, 91], [14, 13, 25, 92], [14, 13, 25, 93], [14, 13, 25, 95], [14, 13, 25, 96], [14, 13, 25, 97], [14, 13, 25, 98], [14, 13, 25, 99], [14, 13, 25, 101], [14, 13, 25, 103], [14, 13, 25, 104], [14, 13, 25, 105], [14, 13, 25, 107], [14, 13, 26, 86], [14, 13, 26, 87], [14, 13, 26, 88], [14, 13, 26, 89], [14, 13, 26, 90], [14, 13, 26, 91], [14, 13, 26, 92], [14, 13, 26, 93], [14, 13, 26, 94], [14, 13, 26, 95], [14, 13, 26, 96], [14, 13, 26, 97], [14, 13, 26, 98], [14, 13, 26, 99], [14, 13, 26, 100], [14, 13, 26, 101], [14, 13, 26, 102], [14, 13, 26, 103], [14, 13, 26, 104], [14, 13, 26, 105], [14, 13, 26, 106], [14, 13, 26, 107], [14, 13, 26, 108], [14, 13, 26, 110], [14, 13, 27, 91], [14, 13, 27, 92], [14, 13, 27, 95], [14, 13, 27, 98], [14, 13, 27, 99], [14, 13, 27, 100], [14, 13, 27, 103], [14, 13, 27, 104], [14, 13, 27, 105], [14, 13, 27, 107], [14, 13, 27, 109], [14, 13, 27, 113], [14, 13, 27, 116], [14, 13, 27, 121], [14, 13, 27, 126], [14, 13, 27, 131], [14, 13, 27, 136], [14, 13, 27, 141], [14, 13, 28, 101], [14, 13, 28, 104], [14, 13, 28, 105], [14, 13, 28, 107], [14, 13, 28, 108], [14, 13, 28, 109], [14, 13, 28, 111], [14, 13, 28, 113], [14, 13, 28, 116], [14, 13, 28, 117], [14, 13, 28, 119], [14, 13, 28, 120], [14, 13, 28, 121], [14, 13, 28, 122], [14, 13, 28, 123], [14, 13, 28, 124], [14, 13, 28, 125], [14, 13, 28, 126], [14, 13, 28, 129], [14, 13, 28, 130], [14, 13, 28, 131], [14, 13, 28, 134], [14, 13, 28, 135], [14, 13, 28, 136], [14, 13, 28, 139], [14, 13, 28, 140], [14, 13, 28, 144], [14, 13, 29, 108], [14, 13, 29, 109], [14, 13, 29, 110], [14, 13, 29, 112], [14, 13, 29, 113], [14, 13, 29, 115], [14, 13, 29, 116], [14, 13, 29, 119], [14, 13, 29, 120], [14, 13, 29, 123], [14, 13, 29, 124], [14, 13, 29, 125], [14, 13, 29, 126], [14, 13, 29, 127], [14, 13, 29, 128], [14, 13, 29, 129], [14, 13, 29, 130], [14, 13, 29, 131], [14, 13, 29, 132], [14, 13, 29, 133], [14, 13, 29, 134], [14, 13, 29, 135], [14, 13, 29, 137], [14, 13, 29, 138], [14, 13, 29, 139], [14, 13, 29, 142], [14, 13, 29, 143], [14, 13, 29, 147], [14, 13, 30, 122], [14, 13, 30, 128], [14, 13, 30, 130], [14, 13, 30, 132], [14, 13, 30, 133], [14, 13, 30, 134], [14, 13, 30, 135], [14, 13, 30, 138], [14, 13, 30, 140], [14, 13, 30, 142], [14, 13, 30, 143], [14, 13, 30, 144], [14, 13, 30, 145], [14, 13, 30, 147], [14, 13, 30, 148], [14, 13, 30, 150], [14, 13, 30, 153], [14, 13, 31, 129], [14, 13, 31, 134], [14, 13, 31, 135], [14, 13, 31, 137], [14, 13, 31, 140], [14, 13, 31, 141], [14, 13, 31, 143], [14, 13, 31, 144], [14, 13, 31, 146], [14, 13, 31, 147], [14, 13, 31, 150], [14, 13, 31, 152], [14, 13, 31, 153], [14, 13, 31, 156], [14, 13, 32, 131], [14, 13, 32, 135], [14, 13, 32, 151], [14, 13, 32, 155], [14, 13, 33, 143], [14, 13, 33, 146], [14, 13, 33, 149], [14, 13, 33, 151], [14, 13, 33, 156], [14, 13, 33, 158], [14, 13, 33, 164], [14, 13, 33, 165], [14, 13, 33, 166], [14, 13, 33, 167], [14, 13, 33, 169], [14, 13, 33, 171], [14, 13, 33, 179], [14, 13, 33, 185], [14, 13, 33, 191], [14, 13, 33, 197], [14, 13, 33, 203], [14, 13, 34, 158], [14, 13, 34, 170], [14, 13, 34, 174], [14, 13, 34, 182], [14, 13, 34, 183], [14, 13, 34, 184], [14, 13, 34, 188], [14, 13, 34, 189], [14, 13, 34, 190], [14, 13, 34, 194], [14, 13, 34, 195], [14, 13, 34, 196], [14, 13, 34, 200], [14, 13, 34, 201], [14, 13, 34, 206], [14, 13, 35, 187], [14, 13, 35, 192], [14, 13, 35, 194], [14, 13, 35, 197], [14, 13, 35, 199], [14, 13, 35, 204], [14, 13, 35, 209], [14, 13, 36, 191], [14, 13, 36, 193], [14, 13, 36, 197], [14, 13, 36, 205], [14, 13, 36, 207], [14, 13, 36, 209], [14, 13, 36, 211], [14, 13, 36, 215], [14, 13, 37, 176], [14, 13, 37, 200], [14, 13, 37, 201], [14, 13, 37, 203], [14, 13, 37, 210], [14, 13, 37, 218], [14, 13, 39, 209], [14, 13, 39, 230], [14, 13, 39, 233], [14, 13, 40, 263], [14, 13, 40, 270], [14, 13, 40, 277], [14, 13, 40, 284], [14, 13, 41, 266], [14, 13, 41, 267], [14, 13, 41, 273], [14, 13, 41, 274], [14, 13, 41, 275], [14, 13, 41, 280], [14, 13, 41, 281], [14, 13, 41, 287], [14, 13, 42, 246], [14, 13, 42, 278], [14, 13, 42, 290], [14, 13, 43, 263], [14, 13, 43, 275], [14, 13, 43, 291], [14, 13, 43, 296], [14, 13, 46, 314], [14, 13, 48, 371], [14, 13, 48, 379], [14, 13, 48, 387], [14, 13, 49, 374], [14, 13, 49, 383], [14, 13, 49, 390], [14, 13, 51, 399], [14, 13, 57, 506], [14, 13, 57, 515], [14, 13, 58, 518], [14, 13, 67, 671], [14, 13, 78, 858]} Since there are not enough let's try depth 4 The set of Graham sequences of depth 4 has size 2011 . The sequences are {[14, 13, 12, 11, 10], [14, 13, 13, 14, 18], [14, 13, 13, 15, 23], [14, 13, 13, 15, 24], [14, 13, 13, 16, 29], [14, 13, 13, 16, 30], [14, 13, 13, 16, 31], [14, 13, 14, 17, 26], [14, 13, 14, 18, 31], [14, 13, 14, 18, 32], [14, 13, 14, 18, 33], [14, 13, 14, 19, 36], [14, 13, 14, 19, 37], [14, 13, 14, 19, 38], [14, 13, 14, 19, 39], [14, 13, 14, 19, 40], [14, 13, 14, 19, 41], [14, 13, 14, 20, 42], [14, 13, 14, 20, 43], [14, 13, 14, 20, 44], [14, 13, 14, 20, 45], [14, 13, 14, 20, 46], [14, 13, 14, 20, 47], [14, 13, 14, 20, 48], [14, 13, 14, 20, 49], [14, 13, 14, 21, 48], [14, 13, 14, 21, 49], [14, 13, 14, 21, 50], [14, 13, 14, 21, 51], [14, 13, 14, 21, 52], [14, 13, 14, 21, 54], [14, 13, 14, 21, 55], [14, 13, 14, 21, 56], [14, 13, 14, 22, 61], [14, 13, 14, 22, 62], [14, 13, 14, 22, 63], [14, 13, 14, 22, 64], [14, 13, 15, 21, 40], [14, 13, 15, 21, 41], [14, 13, 15, 22, 45], [14, 13, 15, 22, 46], [14, 13, 15, 22, 47], [14, 13, 15, 22, 48], [14, 13, 15, 22, 49], [14, 13, 15, 23, 50], [14, 13, 15, 23, 51], [14, 13, 15, 23, 52], [14, 13, 15, 23, 53], [14, 13, 15, 23, 54], [14, 13, 15, 23, 55], [14, 13, 15, 23, 56], [14, 13, 15, 23, 57], [14, 13, 15, 23, 58], [14, 13, 15, 23, 61], [14, 13, 15, 24, 57], [14, 13, 15, 24, 58], [14, 13, 15, 24, 59], [14, 13, 15, 24, 60], [14, 13, 15, 24, 61], [14, 13, 15, 24, 62], [14, 13, 15, 24, 63], [14, 13, 15, 24, 64], [14, 13, 15, 24, 65], [14, 13, 15, 24, 66], [14, 13, 15, 24, 68], [14, 13, 15, 25, 64], [14, 13, 15, 25, 66], [14, 13, 15, 25, 67], [14, 13, 15, 25, 68], [14, 13, 15, 25, 69], [14, 13, 15, 25, 70], [14, 13, 15, 25, 71], [14, 13, 15, 25, 72], [14, 13, 15, 25, 73], [14, 13, 15, 25, 74], [14, 13, 15, 25, 75], [14, 13, 15, 25, 76], [14, 13, 15, 25, 78], [14, 13, 15, 26, 73], [14, 13, 15, 26, 74], [14, 13, 15, 26, 75], [14, 13, 15, 26, 76], [14, 13, 15, 26, 79], [14, 13, 15, 26, 80], [14, 13, 15, 26, 81], [14, 13, 15, 26, 82], [14, 13, 15, 26, 83], [14, 13, 15, 27, 81], [14, 13, 15, 27, 86], [14, 13, 15, 27, 87], [14, 13, 15, 27, 88], [14, 13, 15, 27, 92], [14, 13, 15, 27, 94], [14, 13, 15, 27, 96], [14, 13, 15, 28, 94], [14, 13, 15, 29, 109], [14, 13, 15, 29, 111], [14, 13, 15, 29, 113], [14, 13, 15, 29, 115], [14, 13, 16, 25, 56], [14, 13, 16, 25, 57], [14, 13, 16, 26, 62], [14, 13, 16, 26, 63], [14, 13, 16, 26, 64], [14, 13, 16, 26, 65], [14, 13, 16, 26, 66], [14, 13, 16, 26, 69], [14, 13, 16, 27, 69], [14, 13, 16, 27, 70], [14, 13, 16, 27, 71], [14, 13, 16, 27, 72], [14, 13, 16, 27, 73], [14, 13, 16, 27, 74], [14, 13, 16, 27, 75], [14, 13, 16, 27, 76], [14, 13, 16, 27, 77], [14, 13, 16, 28, 76], [14, 13, 16, 28, 77], [14, 13, 16, 28, 78], [14, 13, 16, 28, 79], [14, 13, 16, 28, 80], [14, 13, 16, 28, 81], [14, 13, 16, 28, 82], [14, 13, 16, 28, 83], [14, 13, 16, 28, 84], [14, 13, 16, 28, 86], [14, 13, 16, 28, 88], [14, 13, 16, 29, 84], [14, 13, 16, 29, 85], [14, 13, 16, 29, 86], [14, 13, 16, 29, 87], [14, 13, 16, 29, 88], [14, 13, 16, 29, 89], [14, 13, 16, 29, 90], [14, 13, 16, 29, 91], [14, 13, 16, 29, 92], [14, 13, 16, 29, 93], [14, 13, 16, 29, 94], [14, 13, 16, 29, 95], [14, 13, 16, 29, 99], [14, 13, 16, 30, 92], [14, 13, 16, 30, 93], [14, 13, 16, 30, 94], [14, 13, 16, 30, 95], [14, 13, 16, 30, 96], [14, 13, 16, 30, 97], [14, 13, 16, 30, 98], [14, 13, 16, 30, 99], [14, 13, 16, 30, 100], [14, 13, 16, 30, 101], [14, 13, 16, 30, 102], [14, 13, 16, 30, 103], [14, 13, 16, 30, 104], [14, 13, 16, 30, 106], [14, 13, 16, 30, 107], [14, 13, 16, 30, 108], [14, 13, 16, 30, 109], [14, 13, 16, 31, 104], [14, 13, 16, 31, 105], [14, 13, 16, 31, 106], [14, 13, 16, 31, 107], [14, 13, 16, 31, 108], [14, 13, 16, 31, 109], [14, 13, 16, 31, 110], [14, 13, 16, 31, 111], [14, 13, 16, 31, 112], [14, 13, 16, 31, 115], [14, 13, 16, 31, 116], [14, 13, 16, 31, 117], [14, 13, 16, 32, 110], [14, 13, 16, 32, 111], [14, 13, 16, 32, 112], [14, 13, 16, 32, 113], [14, 13, 16, 32, 114], [14, 13, 16, 32, 115], [14, 13, 16, 32, 116], [14, 13, 16, 32, 117], [14, 13, 16, 32, 119], [14, 13, 16, 32, 121], [14, 13, 16, 32, 123], [14, 13, 16, 32, 124], [14, 13, 16, 32, 125], [14, 13, 16, 32, 126], [14, 13, 16, 32, 128], [14, 13, 16, 33, 122], [14, 13, 16, 33, 123], [14, 13, 16, 33, 124], [14, 13, 16, 33, 125], [14, 13, 16, 33, 126], [14, 13, 16, 33, 127], [14, 13, 16, 33, 128], [14, 13, 16, 33, 132], [14, 13, 16, 33, 133], [14, 13, 16, 33, 134], [14, 13, 16, 33, 135], [14, 13, 16, 33, 136], [14, 13, 16, 34, 128], [14, 13, 16, 34, 131], [14, 13, 16, 34, 132], [14, 13, 16, 34, 140], [14, 13, 16, 34, 141], [14, 13, 16, 34, 142], [14, 13, 16, 34, 143], [14, 13, 16, 34, 144], [14, 13, 16, 34, 146], [14, 13, 16, 34, 148], [14, 13, 16, 35, 150], [14, 13, 16, 35, 151], [14, 13, 16, 35, 152], [14, 13, 16, 35, 153], [14, 13, 16, 35, 154], [14, 13, 16, 35, 155], [14, 13, 16, 36, 158], [14, 13, 16, 36, 159], [14, 13, 16, 36, 160], [14, 13, 16, 36, 161], [14, 13, 17, 30, 83], [14, 13, 17, 30, 84], [14, 13, 17, 30, 85], [14, 13, 17, 31, 88], [14, 13, 17, 31, 89], [14, 13, 17, 31, 90], [14, 13, 17, 31, 91], [14, 13, 17, 31, 92], [14, 13, 17, 31, 93], [14, 13, 17, 31, 94], [14, 13, 17, 31, 96], [14, 13, 17, 32, 95], [14, 13, 17, 32, 96], [14, 13, 17, 32, 97], [14, 13, 17, 32, 98], [14, 13, 17, 32, 99], [14, 13, 17, 32, 100], [14, 13, 17, 32, 101], [14, 13, 17, 32, 102], [14, 13, 17, 32, 103], [14, 13, 17, 32, 104], [14, 13, 17, 32, 107], [14, 13, 17, 33, 103], [14, 13, 17, 33, 104], [14, 13, 17, 33, 105], [14, 13, 17, 33, 106], [14, 13, 17, 33, 107], [14, 13, 17, 33, 108], [14, 13, 17, 33, 109], [14, 13, 17, 33, 110], [14, 13, 17, 33, 111], [14, 13, 17, 33, 112], [14, 13, 17, 33, 113], [14, 13, 17, 33, 114], [14, 13, 17, 33, 115], [14, 13, 17, 33, 116], [14, 13, 17, 33, 117], [14, 13, 17, 34, 112], [14, 13, 17, 34, 113], [14, 13, 17, 34, 114], [14, 13, 17, 34, 115], [14, 13, 17, 34, 116], [14, 13, 17, 34, 117], [14, 13, 17, 34, 118], [14, 13, 17, 34, 119], [14, 13, 17, 34, 120], [14, 13, 17, 34, 121], [14, 13, 17, 34, 122], [14, 13, 17, 34, 123], [14, 13, 17, 34, 124], [14, 13, 17, 34, 125], [14, 13, 17, 34, 126], [14, 13, 17, 34, 127], [14, 13, 17, 34, 128], [14, 13, 17, 35, 120], [14, 13, 17, 35, 121], [14, 13, 17, 35, 122], [14, 13, 17, 35, 123], [14, 13, 17, 35, 124], [14, 13, 17, 35, 125], [14, 13, 17, 35, 126], [14, 13, 17, 35, 127], [14, 13, 17, 35, 128], [14, 13, 17, 35, 129], [14, 13, 17, 35, 130], [14, 13, 17, 35, 131], [14, 13, 17, 35, 132], [14, 13, 17, 35, 133], [14, 13, 17, 35, 134], [14, 13, 17, 35, 135], [14, 13, 17, 35, 136], [14, 13, 17, 35, 138], [14, 13, 17, 36, 129], [14, 13, 17, 36, 130], [14, 13, 17, 36, 132], [14, 13, 17, 36, 133], [14, 13, 17, 36, 134], [14, 13, 17, 36, 135], [14, 13, 17, 36, 136], [14, 13, 17, 36, 137], [14, 13, 17, 36, 138], [14, 13, 17, 36, 139], [14, 13, 17, 36, 140], [14, 13, 17, 36, 141], [14, 13, 17, 36, 142], [14, 13, 17, 36, 143], [14, 13, 17, 36, 144], [14, 13, 17, 36, 145], [14, 13, 17, 36, 146], [14, 13, 17, 36, 149], [14, 13, 17, 37, 138], [14, 13, 17, 37, 140], [14, 13, 17, 37, 143], [14, 13, 17, 37, 144], [14, 13, 17, 37, 145], [14, 13, 17, 37, 146], [14, 13, 17, 37, 147], [14, 13, 17, 37, 148], [14, 13, 17, 37, 149], [14, 13, 17, 37, 150], [14, 13, 17, 37, 151], [14, 13, 17, 37, 152], [14, 13, 17, 37, 153], [14, 13, 17, 37, 154], [14, 13, 17, 37, 155], [14, 13, 17, 37, 156], [14, 13, 17, 37, 157], [14, 13, 17, 37, 158], [14, 13, 17, 37, 161], [14, 13, 17, 38, 148], [14, 13, 17, 38, 149], [14, 13, 17, 38, 152], [14, 13, 17, 38, 154], [14, 13, 17, 38, 156], [14, 13, 17, 38, 157], [14, 13, 17, 38, 158], [14, 13, 17, 38, 159], [14, 13, 17, 38, 160], [14, 13, 17, 38, 161], [14, 13, 17, 38, 162], [14, 13, 17, 38, 163], [14, 13, 17, 38, 164], [14, 13, 17, 38, 165], [14, 13, 17, 38, 167], [14, 13, 17, 38, 168], [14, 13, 17, 38, 169], [14, 13, 17, 39, 164], [14, 13, 17, 39, 165], [14, 13, 17, 39, 166], [14, 13, 17, 39, 167], [14, 13, 17, 39, 168], [14, 13, 17, 39, 169], [14, 13, 17, 39, 171], [14, 13, 17, 39, 172], [14, 13, 17, 39, 173], [14, 13, 17, 39, 174], [14, 13, 17, 39, 175], [14, 13, 17, 39, 176], [14, 13, 17, 39, 177], [14, 13, 17, 39, 180], [14, 13, 17, 39, 182], [14, 13, 17, 40, 173], [14, 13, 17, 40, 176], [14, 13, 17, 40, 177], [14, 13, 17, 40, 179], [14, 13, 17, 40, 180], [14, 13, 17, 40, 182], [14, 13, 17, 40, 183], [14, 13, 17, 40, 186], [14, 13, 17, 40, 187], [14, 13, 17, 40, 188], [14, 13, 17, 40, 189], [14, 13, 17, 41, 182], [14, 13, 17, 41, 184], [14, 13, 17, 41, 189], [14, 13, 17, 41, 193], [14, 13, 17, 41, 194], [14, 13, 17, 41, 195], [14, 13, 17, 42, 200], [14, 13, 18, 34, 101], [14, 13, 18, 34, 102], [14, 13, 18, 35, 107], [14, 13, 18, 35, 108], [14, 13, 18, 35, 109], [14, 13, 18, 35, 110], [14, 13, 18, 35, 112], [14, 13, 18, 35, 113], [14, 13, 18, 36, 115], [14, 13, 18, 36, 116], [14, 13, 18, 36, 117], [14, 13, 18, 36, 119], [14, 13, 18, 36, 122], [14, 13, 18, 36, 125], [14, 13, 18, 36, 126], [14, 13, 18, 37, 123], [14, 13, 18, 37, 124], [14, 13, 18, 37, 125], [14, 13, 18, 37, 126], [14, 13, 18, 37, 127], [14, 13, 18, 37, 128], [14, 13, 18, 37, 129], [14, 13, 18, 37, 130], [14, 13, 18, 37, 131], [14, 13, 18, 37, 132], [14, 13, 18, 37, 133], [14, 13, 18, 37, 134], [14, 13, 18, 37, 135], [14, 13, 18, 37, 136], [14, 13, 18, 38, 132], [14, 13, 18, 38, 133], [14, 13, 18, 38, 134], [14, 13, 18, 38, 136], [14, 13, 18, 38, 137], [14, 13, 18, 38, 138], [14, 13, 18, 38, 139], [14, 13, 18, 38, 140], [14, 13, 18, 38, 141], [14, 13, 18, 38, 142], [14, 13, 18, 38, 143], [14, 13, 18, 38, 144], [14, 13, 18, 38, 146], [14, 13, 18, 39, 140], [14, 13, 18, 39, 141], [14, 13, 18, 39, 142], [14, 13, 18, 39, 143], [14, 13, 18, 39, 144], [14, 13, 18, 39, 145], [14, 13, 18, 39, 146], [14, 13, 18, 39, 147], [14, 13, 18, 39, 148], [14, 13, 18, 39, 149], [14, 13, 18, 39, 150], [14, 13, 18, 39, 151], [14, 13, 18, 39, 152], [14, 13, 18, 39, 153], [14, 13, 18, 39, 155], [14, 13, 18, 39, 156], [14, 13, 18, 39, 157], [14, 13, 18, 40, 150], [14, 13, 18, 40, 152], [14, 13, 18, 40, 153], [14, 13, 18, 40, 154], [14, 13, 18, 40, 155], [14, 13, 18, 40, 156], [14, 13, 18, 40, 157], [14, 13, 18, 40, 158], [14, 13, 18, 40, 159], [14, 13, 18, 40, 160], [14, 13, 18, 40, 161], [14, 13, 18, 40, 162], [14, 13, 18, 40, 163], [14, 13, 18, 40, 164], [14, 13, 18, 40, 165], [14, 13, 18, 40, 166], [14, 13, 18, 40, 167], [14, 13, 18, 40, 169], [14, 13, 18, 41, 158], [14, 13, 18, 41, 160], [14, 13, 18, 41, 162], [14, 13, 18, 41, 164], [14, 13, 18, 41, 165], [14, 13, 18, 41, 166], [14, 13, 18, 41, 167], [14, 13, 18, 41, 168], [14, 13, 18, 41, 169], [14, 13, 18, 41, 170], [14, 13, 18, 41, 171], [14, 13, 18, 41, 172], [14, 13, 18, 41, 173], [14, 13, 18, 41, 174], [14, 13, 18, 41, 175], [14, 13, 18, 41, 176], [14, 13, 18, 41, 177], [14, 13, 18, 41, 178], [14, 13, 18, 41, 179], [14, 13, 18, 41, 187], [14, 13, 18, 41, 190], [14, 13, 18, 42, 172], [14, 13, 18, 42, 173], [14, 13, 18, 42, 174], [14, 13, 18, 42, 176], [14, 13, 18, 42, 177], [14, 13, 18, 42, 178], [14, 13, 18, 42, 181], [14, 13, 18, 42, 182], [14, 13, 18, 42, 183], [14, 13, 18, 42, 184], [14, 13, 18, 42, 185], [14, 13, 18, 42, 186], [14, 13, 18, 42, 188], [14, 13, 18, 42, 192], [14, 13, 18, 43, 174], [14, 13, 18, 43, 175], [14, 13, 18, 43, 180], [14, 13, 18, 43, 181], [14, 13, 18, 43, 182], [14, 13, 18, 43, 184], [14, 13, 18, 43, 185], [14, 13, 18, 43, 188], [14, 13, 18, 43, 189], [14, 13, 18, 43, 190], [14, 13, 18, 43, 192], [14, 13, 18, 43, 193], [14, 13, 18, 43, 194], [14, 13, 18, 43, 195], [14, 13, 18, 43, 196], [14, 13, 18, 43, 197], [14, 13, 18, 43, 203], [14, 13, 18, 43, 204], [14, 13, 18, 43, 205], [14, 13, 18, 43, 206], [14, 13, 18, 43, 207], [14, 13, 18, 44, 194], [14, 13, 18, 44, 199], [14, 13, 18, 44, 200], [14, 13, 18, 44, 201], [14, 13, 18, 44, 202], [14, 13, 18, 44, 207], [14, 13, 18, 44, 210], [14, 13, 18, 44, 211], [14, 13, 18, 44, 217], [14, 13, 18, 44, 220], [14, 13, 18, 44, 223], [14, 13, 18, 45, 195], [14, 13, 18, 45, 211], [14, 13, 18, 45, 212], [14, 13, 18, 45, 214], [14, 13, 18, 45, 216], [14, 13, 18, 45, 217], [14, 13, 18, 45, 222], [14, 13, 18, 45, 223], [14, 13, 18, 45, 224], [14, 13, 18, 45, 226], [14, 13, 18, 45, 228], [14, 13, 18, 46, 229], [14, 13, 18, 46, 230], [14, 13, 18, 47, 240], [14, 13, 18, 47, 241], [14, 13, 18, 47, 242], [14, 13, 18, 47, 243], [14, 13, 18, 47, 251], [14, 13, 18, 47, 254], [14, 13, 18, 47, 257], [14, 13, 18, 49, 259], [14, 13, 18, 50, 283], [14, 13, 18, 50, 286], [14, 13, 18, 50, 289], [14, 13, 18, 50, 292], [14, 13, 18, 51, 276], [14, 13, 18, 53, 316], [14, 13, 18, 53, 319], [14, 13, 18, 53, 322], [14, 13, 19, 39, 126], [14, 13, 19, 39, 128], [14, 13, 19, 40, 134], [14, 13, 19, 40, 137], [14, 13, 19, 40, 139], [14, 13, 19, 40, 141], [14, 13, 19, 41, 143], [14, 13, 19, 41, 144], [14, 13, 19, 41, 146], [14, 13, 19, 41, 147], [14, 13, 19, 41, 148], [14, 13, 19, 41, 149], [14, 13, 19, 41, 150], [14, 13, 19, 42, 151], [14, 13, 19, 42, 154], [14, 13, 19, 42, 155], [14, 13, 19, 42, 156], [14, 13, 19, 42, 157], [14, 13, 19, 42, 158], [14, 13, 19, 42, 159], [14, 13, 19, 42, 160], [14, 13, 19, 42, 161], [14, 13, 19, 42, 162], [14, 13, 19, 42, 165], [14, 13, 19, 43, 160], [14, 13, 19, 43, 161], [14, 13, 19, 43, 163], [14, 13, 19, 43, 164], [14, 13, 19, 43, 165], [14, 13, 19, 43, 166], [14, 13, 19, 43, 167], [14, 13, 19, 43, 168], [14, 13, 19, 43, 169], [14, 13, 19, 43, 170], [14, 13, 19, 43, 171], [14, 13, 19, 43, 172], [14, 13, 19, 43, 177], [14, 13, 19, 44, 173], [14, 13, 19, 44, 174], [14, 13, 19, 44, 175], [14, 13, 19, 44, 176], [14, 13, 19, 44, 177], [14, 13, 19, 44, 178], [14, 13, 19, 44, 179], [14, 13, 19, 44, 180], [14, 13, 19, 44, 181], [14, 13, 19, 44, 182], [14, 13, 19, 44, 183], [14, 13, 19, 44, 184], [14, 13, 19, 44, 185], [14, 13, 19, 44, 187], [14, 13, 19, 44, 189], [14, 13, 19, 44, 195], [14, 13, 19, 44, 198], [14, 13, 19, 45, 181], [14, 13, 19, 45, 182], [14, 13, 19, 45, 183], [14, 13, 19, 45, 184], [14, 13, 19, 45, 185], [14, 13, 19, 45, 187], [14, 13, 19, 45, 188], [14, 13, 19, 45, 189], [14, 13, 19, 45, 190], [14, 13, 19, 45, 194], [14, 13, 19, 45, 196], [14, 13, 19, 45, 198], [14, 13, 19, 45, 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2188], [14, 13, 34, 194, 2211], [14, 13, 34, 195, 2217], [14, 13, 34, 195, 2222], [14, 13, 34, 196, 2228], [14, 13, 34, 200, 2318], [14, 13, 34, 201, 2323], [14, 13, 34, 206, 2420], [14, 13, 35, 187, 2000], [14, 13, 35, 192, 2120], [14, 13, 35, 194, 2140], [14, 13, 35, 194, 2147], [14, 13, 35, 197, 2225], [14, 13, 35, 199, 2240], [14, 13, 35, 204, 2360], [14, 13, 35, 209, 2457], [14, 13, 36, 191, 2014], [14, 13, 36, 193, 2041], [14, 13, 36, 197, 2131], [14, 13, 36, 205, 2329], [14, 13, 36, 207, 2349], [14, 13, 36, 209, 2419], [14, 13, 36, 211, 2434], [14, 13, 36, 215, 2521], [14, 13, 37, 176, 1520], [14, 13, 37, 200, 2096], [14, 13, 37, 201, 2120], [14, 13, 37, 203, 2198], [14, 13, 37, 210, 2366], [14, 13, 37, 218, 2558], [14, 13, 39, 209, 2161], [14, 13, 39, 230, 2665], [14, 13, 39, 233, 2737], [14, 13, 40, 263, 3426], [14, 13, 40, 270, 3566], [14, 13, 40, 270, 3573], [14, 13, 40, 277, 3707], [14, 13, 40, 284, 3842], [14, 13, 41, 266, 3434], [14, 13, 41, 267, 3446], [14, 13, 41, 273, 3581], [14, 13, 41, 274, 3614], [14, 13, 41, 275, 3626], [14, 13, 41, 280, 3749], [14, 13, 41, 281, 3754], [14, 13, 41, 287, 3884], [14, 13, 42, 246, 2790], [14, 13, 42, 278, 3638], [14, 13, 42, 290, 3926], [14, 13, 43, 263, 3143], [14, 13, 43, 275, 3491], [14, 13, 43, 291, 3875], [14, 13, 43, 296, 3995], [14, 13, 46, 314, 4226], [14, 13, 48, 371, 5590], [14, 13, 48, 379, 5770], [14, 13, 48, 387, 5943], [14, 13, 49, 374, 5606], [14, 13, 49, 383, 5822], [14, 13, 49, 390, 5990], [14, 13, 51, 399, 6111], [14, 13, 57, 506, 8650], [14, 13, 57, 515, 8866], [14, 13, 58, 518, 8918], [14, 13, 67, 671, 12815], [14, 13, 78, 858, 18018]} There are 7741 unlabeled trees on 15 vertices The set of Graham sequences of depth 3 has size 702. The sequences are {[15, 14, 13, 12], [15, 14, 14, 15], [15, 14, 14, 16], [15, 14, 14, 17], [15, 14, 15, 18], [15, 14, 15, 19], [15, 14, 15, 20], [15, 14, 15, 21], [15, 14, 15, 22], [15, 14, 15, 23], [15, 14, 16, 22], [15, 14, 16, 23], [15, 14, 16, 24], [15, 14, 16, 25], [15, 14, 16, 26], [15, 14, 16, 27], [15, 14, 16, 28], [15, 14, 16, 29], [15, 14, 16, 30], [15, 14, 17, 26], [15, 14, 17, 27], [15, 14, 17, 28], [15, 14, 17, 29], [15, 14, 17, 30], [15, 14, 17, 31], [15, 14, 17, 32], [15, 14, 17, 33], [15, 14, 17, 34], [15, 14, 17, 35], [15, 14, 17, 36], [15, 14, 17, 37], [15, 14, 18, 31], [15, 14, 18, 32], [15, 14, 18, 33], [15, 14, 18, 34], [15, 14, 18, 35], [15, 14, 18, 36], [15, 14, 18, 37], [15, 14, 18, 38], [15, 14, 18, 39], [15, 14, 18, 40], [15, 14, 18, 41], [15, 14, 18, 42], [15, 14, 18, 43], [15, 14, 18, 44], [15, 14, 19, 35], [15, 14, 19, 36], [15, 14, 19, 37], [15, 14, 19, 38], [15, 14, 19, 39], [15, 14, 19, 40], [15, 14, 19, 41], [15, 14, 19, 42], [15, 14, 19, 43], [15, 14, 19, 44], [15, 14, 19, 45], [15, 14, 19, 46], [15, 14, 19, 47], [15, 14, 19, 48], [15, 14, 19, 50], [15, 14, 19, 51], [15, 14, 19, 52], [15, 14, 19, 54], [15, 14, 20, 40], [15, 14, 20, 41], [15, 14, 20, 42], [15, 14, 20, 43], [15, 14, 20, 44], [15, 14, 20, 45], [15, 14, 20, 46], [15, 14, 20, 47], [15, 14, 20, 48], [15, 14, 20, 49], [15, 14, 20, 50], [15, 14, 20, 51], [15, 14, 20, 52], [15, 14, 20, 53], [15, 14, 20, 54], [15, 14, 20, 55], [15, 14, 20, 56], [15, 14, 20, 57], [15, 14, 20, 58], [15, 14, 20, 59], [15, 14, 20, 60], [15, 14, 20, 61], [15, 14, 20, 62], [15, 14, 21, 44], [15, 14, 21, 45], [15, 14, 21, 46], [15, 14, 21, 47], [15, 14, 21, 48], [15, 14, 21, 49], [15, 14, 21, 50], [15, 14, 21, 51], [15, 14, 21, 52], [15, 14, 21, 53], [15, 14, 21, 54], [15, 14, 21, 55], [15, 14, 21, 56], [15, 14, 21, 57], [15, 14, 21, 58], [15, 14, 21, 59], [15, 14, 21, 60], [15, 14, 21, 61], [15, 14, 21, 62], [15, 14, 21, 63], [15, 14, 21, 64], [15, 14, 21, 65], [15, 14, 21, 66], [15, 14, 21, 67], [15, 14, 21, 68], [15, 14, 22, 50], [15, 14, 22, 52], [15, 14, 22, 53], [15, 14, 22, 54], [15, 14, 22, 55], [15, 14, 22, 56], [15, 14, 22, 57], [15, 14, 22, 58], [15, 14, 22, 59], [15, 14, 22, 60], [15, 14, 22, 61], [15, 14, 22, 62], [15, 14, 22, 63], [15, 14, 22, 64], [15, 14, 22, 65], [15, 14, 22, 66], [15, 14, 22, 67], [15, 14, 22, 68], [15, 14, 22, 69], [15, 14, 22, 70], [15, 14, 22, 71], [15, 14, 22, 72], [15, 14, 22, 73], [15, 14, 22, 74], [15, 14, 22, 75], [15, 14, 22, 76], [15, 14, 23, 55], [15, 14, 23, 56], [15, 14, 23, 57], [15, 14, 23, 58], [15, 14, 23, 59], [15, 14, 23, 60], [15, 14, 23, 61], [15, 14, 23, 62], [15, 14, 23, 63], [15, 14, 23, 64], [15, 14, 23, 65], [15, 14, 23, 66], [15, 14, 23, 67], [15, 14, 23, 68], [15, 14, 23, 69], [15, 14, 23, 70], [15, 14, 23, 71], [15, 14, 23, 72], [15, 14, 23, 73], [15, 14, 23, 74], [15, 14, 23, 75], [15, 14, 23, 76], [15, 14, 23, 77], [15, 14, 23, 78], [15, 14, 23, 79], [15, 14, 23, 80], [15, 14, 23, 84], [15, 14, 23, 88], [15, 14, 23, 92], [15, 14, 24, 63], [15, 14, 24, 64], [15, 14, 24, 65], [15, 14, 24, 66], [15, 14, 24, 67], [15, 14, 24, 68], [15, 14, 24, 69], [15, 14, 24, 70], [15, 14, 24, 71], [15, 14, 24, 72], [15, 14, 24, 73], [15, 14, 24, 74], [15, 14, 24, 75], [15, 14, 24, 76], [15, 14, 24, 77], [15, 14, 24, 78], [15, 14, 24, 79], [15, 14, 24, 80], [15, 14, 24, 81], [15, 14, 24, 82], [15, 14, 24, 83], [15, 14, 24, 84], [15, 14, 24, 85], [15, 14, 24, 87], [15, 14, 24, 88], [15, 14, 24, 89], [15, 14, 24, 91], [15, 14, 24, 92], [15, 14, 24, 93], [15, 14, 24, 95], [15, 14, 24, 96], [15, 14, 24, 97], [15, 14, 24, 99], [15, 14, 24, 100], [15, 14, 25, 68], [15, 14, 25, 69], [15, 14, 25, 70], [15, 14, 25, 71], [15, 14, 25, 72], [15, 14, 25, 73], [15, 14, 25, 74], [15, 14, 25, 75], [15, 14, 25, 76], [15, 14, 25, 77], [15, 14, 25, 78], [15, 14, 25, 79], [15, 14, 25, 80], [15, 14, 25, 81], [15, 14, 25, 82], [15, 14, 25, 83], [15, 14, 25, 84], [15, 14, 25, 85], [15, 14, 25, 86], [15, 14, 25, 87], [15, 14, 25, 88], [15, 14, 25, 89], [15, 14, 25, 90], [15, 14, 25, 91], [15, 14, 25, 92], [15, 14, 25, 93], [15, 14, 25, 94], [15, 14, 25, 95], [15, 14, 25, 96], [15, 14, 25, 97], [15, 14, 25, 98], [15, 14, 25, 99], [15, 14, 25, 100], [15, 14, 25, 102], [15, 14, 25, 103], [15, 14, 25, 106], [15, 14, 26, 75], [15, 14, 26, 76], [15, 14, 26, 77], [15, 14, 26, 78], [15, 14, 26, 79], [15, 14, 26, 80], [15, 14, 26, 81], [15, 14, 26, 82], [15, 14, 26, 83], [15, 14, 26, 84], [15, 14, 26, 85], [15, 14, 26, 86], [15, 14, 26, 87], [15, 14, 26, 88], [15, 14, 26, 89], [15, 14, 26, 90], [15, 14, 26, 91], [15, 14, 26, 92], [15, 14, 26, 93], [15, 14, 26, 94], [15, 14, 26, 95], [15, 14, 26, 96], [15, 14, 26, 97], [15, 14, 26, 98], [15, 14, 26, 99], [15, 14, 26, 100], [15, 14, 26, 101], [15, 14, 26, 102], [15, 14, 26, 103], [15, 14, 26, 104], [15, 14, 26, 105], [15, 14, 26, 106], [15, 14, 26, 108], [15, 14, 26, 109], [15, 14, 26, 110], [15, 14, 26, 112], [15, 14, 27, 84], [15, 14, 27, 86], [15, 14, 27, 88], [15, 14, 27, 89], [15, 14, 27, 90], [15, 14, 27, 91], [15, 14, 27, 92], [15, 14, 27, 93], [15, 14, 27, 94], [15, 14, 27, 95], [15, 14, 27, 96], [15, 14, 27, 97], [15, 14, 27, 98], [15, 14, 27, 99], [15, 14, 27, 100], [15, 14, 27, 101], [15, 14, 27, 102], [15, 14, 27, 103], [15, 14, 27, 104], [15, 14, 27, 105], [15, 14, 27, 106], [15, 14, 27, 107], [15, 14, 27, 108], [15, 14, 27, 109], [15, 14, 27, 110], [15, 14, 27, 111], [15, 14, 27, 112], [15, 14, 27, 113], [15, 14, 27, 115], [15, 14, 28, 86], [15, 14, 28, 87], [15, 14, 28, 92], [15, 14, 28, 93], [15, 14, 28, 94], [15, 14, 28, 95], [15, 14, 28, 96], [15, 14, 28, 97], [15, 14, 28, 98], [15, 14, 28, 99], [15, 14, 28, 100], [15, 14, 28, 101], [15, 14, 28, 102], [15, 14, 28, 103], [15, 14, 28, 104], [15, 14, 28, 105], [15, 14, 28, 106], [15, 14, 28, 107], [15, 14, 28, 108], [15, 14, 28, 109], [15, 14, 28, 110], [15, 14, 28, 111], [15, 14, 28, 112], [15, 14, 28, 114], [15, 14, 28, 115], [15, 14, 28, 116], [15, 14, 28, 117], [15, 14, 28, 118], [15, 14, 28, 122], [15, 14, 28, 127], [15, 14, 28, 132], [15, 14, 28, 137], [15, 14, 28, 142], [15, 14, 28, 147], [15, 14, 29, 97], [15, 14, 29, 98], [15, 14, 29, 100], [15, 14, 29, 101], [15, 14, 29, 102], [15, 14, 29, 103], [15, 14, 29, 104], [15, 14, 29, 105], [15, 14, 29, 106], [15, 14, 29, 107], [15, 14, 29, 108], [15, 14, 29, 109], [15, 14, 29, 110], [15, 14, 29, 111], [15, 14, 29, 112], [15, 14, 29, 113], [15, 14, 29, 114], [15, 14, 29, 116], [15, 14, 29, 117], [15, 14, 29, 118], [15, 14, 29, 120], [15, 14, 29, 121], [15, 14, 29, 122], [15, 14, 29, 123], [15, 14, 29, 124], [15, 14, 29, 125], [15, 14, 29, 126], [15, 14, 29, 127], [15, 14, 29, 128], [15, 14, 29, 129], [15, 14, 29, 130], [15, 14, 29, 131], [15, 14, 29, 132], [15, 14, 29, 135], [15, 14, 29, 136], [15, 14, 29, 137], [15, 14, 29, 140], [15, 14, 29, 141], [15, 14, 29, 142], [15, 14, 29, 145], [15, 14, 29, 146], [15, 14, 29, 150], [15, 14, 30, 106], [15, 14, 30, 108], [15, 14, 30, 109], [15, 14, 30, 110], [15, 14, 30, 111], [15, 14, 30, 112], [15, 14, 30, 113], [15, 14, 30, 114], [15, 14, 30, 115], [15, 14, 30, 116], [15, 14, 30, 117], [15, 14, 30, 118], [15, 14, 30, 119], [15, 14, 30, 120], [15, 14, 30, 121], [15, 14, 30, 122], [15, 14, 30, 123], [15, 14, 30, 124], [15, 14, 30, 125], [15, 14, 30, 126], [15, 14, 30, 127], [15, 14, 30, 128], [15, 14, 30, 129], [15, 14, 30, 130], [15, 14, 30, 131], [15, 14, 30, 132], [15, 14, 30, 133], [15, 14, 30, 134], [15, 14, 30, 135], [15, 14, 30, 136], [15, 14, 30, 137], [15, 14, 30, 138], [15, 14, 30, 139], [15, 14, 30, 140], [15, 14, 30, 141], [15, 14, 30, 143], [15, 14, 30, 144], [15, 14, 30, 145], [15, 14, 30, 148], [15, 14, 30, 149], [15, 14, 30, 153], [15, 14, 31, 114], [15, 14, 31, 118], [15, 14, 31, 122], [15, 14, 31, 124], [15, 14, 31, 126], [15, 14, 31, 128], [15, 14, 31, 129], [15, 14, 31, 130], [15, 14, 31, 131], [15, 14, 31, 132], [15, 14, 31, 133], [15, 14, 31, 134], [15, 14, 31, 135], [15, 14, 31, 136], [15, 14, 31, 138], [15, 14, 31, 139], [15, 14, 31, 140], [15, 14, 31, 141], [15, 14, 31, 142], [15, 14, 31, 143], [15, 14, 31, 144], [15, 14, 31, 145], [15, 14, 31, 146], [15, 14, 31, 148], [15, 14, 31, 149], [15, 14, 31, 150], [15, 14, 31, 151], [15, 14, 31, 152], [15, 14, 31, 153], [15, 14, 31, 154], [15, 14, 31, 156], [15, 14, 31, 159], [15, 14, 32, 122], [15, 14, 32, 123], [15, 14, 32, 124], [15, 14, 32, 126], [15, 14, 32, 129], [15, 14, 32, 130], [15, 14, 32, 132], [15, 14, 32, 133], [15, 14, 32, 134], [15, 14, 32, 135], [15, 14, 32, 136], [15, 14, 32, 137], [15, 14, 32, 138], [15, 14, 32, 139], [15, 14, 32, 140], [15, 14, 32, 141], [15, 14, 32, 142], [15, 14, 32, 143], [15, 14, 32, 144], [15, 14, 32, 145], [15, 14, 32, 146], [15, 14, 32, 147], [15, 14, 32, 148], [15, 14, 32, 149], [15, 14, 32, 150], [15, 14, 32, 151], [15, 14, 32, 152], [15, 14, 32, 153], [15, 14, 32, 154], [15, 14, 32, 155], [15, 14, 32, 156], [15, 14, 32, 157], [15, 14, 32, 158], [15, 14, 32, 159], [15, 14, 32, 162], [15, 14, 33, 132], [15, 14, 33, 136], [15, 14, 33, 140], [15, 14, 33, 145], [15, 14, 33, 147], [15, 14, 33, 151], [15, 14, 33, 152], [15, 14, 33, 153], [15, 14, 33, 156], [15, 14, 33, 157], [15, 14, 33, 159], [15, 14, 33, 160], [15, 14, 33, 165], [15, 14, 34, 140], [15, 14, 34, 143], [15, 14, 34, 145], [15, 14, 34, 147], [15, 14, 34, 148], [15, 14, 34, 150], [15, 14, 34, 152], [15, 14, 34, 153], [15, 14, 34, 155], [15, 14, 34, 156], [15, 14, 34, 157], [15, 14, 34, 159], [15, 14, 34, 160], [15, 14, 34, 162], [15, 14, 34, 163], [15, 14, 34, 165], [15, 14, 34, 167], [15, 14, 34, 168], [15, 14, 34, 170], [15, 14, 34, 171], [15, 14, 34, 172], [15, 14, 34, 173], [15, 14, 34, 175], [15, 14, 34, 177], [15, 14, 34, 180], [15, 14, 34, 186], [15, 14, 34, 192], [15, 14, 34, 198], [15, 14, 34, 204], [15, 14, 34, 210], [15, 14, 35, 154], [15, 14, 35, 156], [15, 14, 35, 160], [15, 14, 35, 162], [15, 14, 35, 164], [15, 14, 35, 168], [15, 14, 35, 170], [15, 14, 35, 172], [15, 14, 35, 174], [15, 14, 35, 176], [15, 14, 35, 178], [15, 14, 35, 180], [15, 14, 35, 183], [15, 14, 35, 184], [15, 14, 35, 185], [15, 14, 35, 189], [15, 14, 35, 190], [15, 14, 35, 191], [15, 14, 35, 195], [15, 14, 35, 196], [15, 14, 35, 197], [15, 14, 35, 201], [15, 14, 35, 202], [15, 14, 35, 203], [15, 14, 35, 207], [15, 14, 35, 208], [15, 14, 35, 213], [15, 14, 36, 162], [15, 14, 36, 172], [15, 14, 36, 187], [15, 14, 36, 188], [15, 14, 36, 189], [15, 14, 36, 192], [15, 14, 36, 193], [15, 14, 36, 194], [15, 14, 36, 195], [15, 14, 36, 196], [15, 14, 36, 198], [15, 14, 36, 199], [15, 14, 36, 200], [15, 14, 36, 201], [15, 14, 36, 204], [15, 14, 36, 205], [15, 14, 36, 206], [15, 14, 36, 210], [15, 14, 36, 211], [15, 14, 36, 216], [15, 14, 37, 177], [15, 14, 37, 183], [15, 14, 37, 189], [15, 14, 37, 192], [15, 14, 37, 194], [15, 14, 37, 196], [15, 14, 37, 198], [15, 14, 37, 199], [15, 14, 37, 200], [15, 14, 37, 204], [15, 14, 37, 206], [15, 14, 37, 208], [15, 14, 37, 209], [15, 14, 37, 210], [15, 14, 37, 212], [15, 14, 37, 214], [15, 14, 37, 216], [15, 14, 37, 218], [15, 14, 37, 219], [15, 14, 37, 222], [15, 14, 38, 177], [15, 14, 38, 181], [15, 14, 38, 182], [15, 14, 38, 198], [15, 14, 38, 199], [15, 14, 38, 201], [15, 14, 38, 202], [15, 14, 38, 205], [15, 14, 38, 206], [15, 14, 38, 207], [15, 14, 38, 209], [15, 14, 38, 210], [15, 14, 38, 212], [15, 14, 38, 213], [15, 14, 38, 217], [15, 14, 38, 220], [15, 14, 38, 221], [15, 14, 38, 225], [15, 14, 39, 190], [15, 14, 39, 208], [15, 14, 39, 210], [15, 14, 40, 210], [15, 14, 40, 213], [15, 14, 40, 216], [15, 14, 40, 222], [15, 14, 40, 231], [15, 14, 40, 234], [15, 14, 40, 237], [15, 14, 40, 240], [15, 14, 41, 223], [15, 14, 41, 237], [15, 14, 41, 243], [15, 14, 41, 264], [15, 14, 41, 271], [15, 14, 41, 278], [15, 14, 41, 285], [15, 14, 41, 292], [15, 14, 42, 267], [15, 14, 42, 268], [15, 14, 42, 269], [15, 14, 42, 274], [15, 14, 42, 275], [15, 14, 42, 276], [15, 14, 42, 281], [15, 14, 42, 282], [15, 14, 42, 283], [15, 14, 42, 288], [15, 14, 42, 289], [15, 14, 42, 295], [15, 14, 43, 222], [15, 14, 43, 252], [15, 14, 43, 272], [15, 14, 43, 278], [15, 14, 43, 280], [15, 14, 43, 284], [15, 14, 43, 286], [15, 14, 43, 292], [15, 14, 43, 298], [15, 14, 44, 240], [15, 14, 44, 268], [15, 14, 44, 270], [15, 14, 44, 276], [15, 14, 44, 278], [15, 14, 44, 283], [15, 14, 44, 292], [15, 14, 44, 294], [15, 14, 44, 297], [15, 14, 44, 299], [15, 14, 44, 304], [15, 14, 45, 289], [15, 14, 45, 297], [15, 14, 45, 307], [15, 14, 47, 294], [15, 14, 47, 318], [15, 14, 47, 322], [15, 14, 49, 315], [15, 14, 49, 372], [15, 14, 49, 380], [15, 14, 49, 388], [15, 14, 49, 396], [15, 14, 50, 375], [15, 14, 50, 376], [15, 14, 50, 383], [15, 14, 50, 384], [15, 14, 50, 385], [15, 14, 50, 391], [15, 14, 50, 392], [15, 14, 50, 399], [15, 14, 51, 352], [15, 14, 51, 388], [15, 14, 51, 402], [15, 14, 52, 384], [15, 14, 52, 402], [15, 14, 52, 408], [15, 14, 55, 426], [15, 14, 58, 507], [15, 14, 58, 516], [15, 14, 58, 525], [15, 14, 59, 510], [15, 14, 59, 520], [15, 14, 59, 528], [15, 14, 61, 537], [15, 14, 68, 672], [15, 14, 68, 682], [15, 14, 69, 685], [15, 14, 79, 870], [15, 14, 91, 1092]} Since there are not enough let's try depth 4 The set of Graham sequences of depth 4 has size . The sequences are There are 19320 unlabeled trees on 16 vertices. The set of Graham sequences of depth 3 has size 1041. The sequences are {[16, 15, 14, 13], [16, 15, 15, 16], [16, 15, 15, 17], [16, 15, 15, 18], [16, 15, 16, 19], [16, 15, 16, 20], [16, 15, 16, 21], [16, 15, 16, 22], [16, 15, 16, 23], [16, 15, 16, 24], [16, 15, 17, 23], [16, 15, 17, 24], [16, 15, 17, 25], [16, 15, 17, 26], [16, 15, 17, 27], [16, 15, 17, 28], [16, 15, 17, 29], [16, 15, 17, 30], [16, 15, 17, 31], [16, 15, 18, 27], [16, 15, 18, 28], [16, 15, 18, 29], [16, 15, 18, 30], [16, 15, 18, 31], [16, 15, 18, 32], [16, 15, 18, 33], [16, 15, 18, 34], [16, 15, 18, 35], [16, 15, 18, 36], [16, 15, 18, 37], [16, 15, 18, 38], [16, 15, 19, 31], [16, 15, 19, 32], [16, 15, 19, 33], [16, 15, 19, 34], [16, 15, 19, 35], [16, 15, 19, 36], [16, 15, 19, 37], [16, 15, 19, 38], [16, 15, 19, 39], [16, 15, 19, 40], [16, 15, 19, 41], [16, 15, 19, 42], [16, 15, 19, 43], [16, 15, 19, 44], [16, 15, 19, 45], [16, 15, 20, 36], [16, 15, 20, 37], [16, 15, 20, 38], [16, 15, 20, 39], [16, 15, 20, 40], [16, 15, 20, 41], [16, 15, 20, 42], [16, 15, 20, 43], [16, 15, 20, 44], [16, 15, 20, 45], [16, 15, 20, 46], [16, 15, 20, 47], [16, 15, 20, 48], [16, 15, 20, 49], [16, 15, 20, 50], [16, 15, 20, 51], [16, 15, 20, 52], [16, 15, 20, 53], [16, 15, 20, 55], [16, 15, 21, 41], [16, 15, 21, 42], [16, 15, 21, 43], [16, 15, 21, 44], [16, 15, 21, 45], [16, 15, 21, 46], [16, 15, 21, 47], [16, 15, 21, 48], [16, 15, 21, 49], [16, 15, 21, 50], [16, 15, 21, 51], [16, 15, 21, 52], [16, 15, 21, 53], [16, 15, 21, 54], [16, 15, 21, 55], [16, 15, 21, 56], [16, 15, 21, 57], [16, 15, 21, 58], [16, 15, 21, 59], [16, 15, 21, 60], [16, 15, 21, 61], [16, 15, 21, 62], [16, 15, 21, 63], [16, 15, 22, 45], [16, 15, 22, 46], [16, 15, 22, 47], [16, 15, 22, 48], [16, 15, 22, 49], [16, 15, 22, 50], [16, 15, 22, 51], [16, 15, 22, 52], [16, 15, 22, 53], [16, 15, 22, 54], [16, 15, 22, 55], [16, 15, 22, 56], [16, 15, 22, 57], [16, 15, 22, 58], [16, 15, 22, 59], [16, 15, 22, 60], [16, 15, 22, 61], [16, 15, 22, 62], [16, 15, 22, 63], [16, 15, 22, 64], [16, 15, 22, 65], [16, 15, 22, 66], 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