#Contains integer sequences enumerating normal walks and good walks for the 11 lists of atomic steps we examined. #Can be run with ComboProject3.txt or ComboProject3Extended.txt #Note: SeqW and SeqGW does not include the path from (0,0,0) to (0,0,0). #A 1 should be added before every sequence, and is so in Project3Database.txt AtomicList1 := {[0, 0, 1], [0, 0, 2], [0, 1, 0], [0, 2, 0], [1, 0, 0], [1, 1, 1], [2, 0, 0], [2, 2, 2]}; AtomicList2 := {[0, 0, 1], [0, 1, 0], [1, 0, 0], [1, 1, 1], [2, 2, 2]}; AtomicList3 := {[0, 1, 2], [0, 2, 1], [1, 0, 2], [1, 2, 0], [2, 0, 1], [2, 1, 0]}; AtomicList4 := {[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]}; AtomicList5 := {[0, 0, 1], [0, 0, 2], [0, 0, 3], [0, 1, 0], [0, 2, 0], [0, 3, 0], [1, 0, 0], [1, 1, 1], [2, 0, 0], [2, 2, 2], [3, 0, 0], [3, 3, 3]}; AtomicList6 := {[0, 1, 1], [1, 0, 1], [1, 1, 0]}; AtomicList7 := {[0, 1, 1], [1, 0, 1], [1, 1, 0], [1, 1, 1]}; AtomicList8 := {[0, 1, 1], [0, 2, 2], [1, 0, 1], [1, 1, 0], [2, 0, 2], [2, 2, 0]}; AtomicList9 := {[0, 1, 3], [0, 3, 1], [1, 0, 3], [1, 3, 0], [3, 0, 1], [3, 1, 0]}; AtomicList10 := {seq([0, 0, i], i = 1 .. 50), seq([0, i, 0], i = 1 .. 50), seq([i, 0, 0], i = 1 .. 50)}; AtomicList11 := {seq([0, 0, i], i = 1 .. 50), seq([0, i, 0], i = 1 .. 50), seq([i, 0, 0], i = 1 .. 50), seq([i, i, i], i = 1 .. 50)}; #Normal paths: SeqW(AtomicList1, 20); [7, 248, 9741, 426719, 19725956, 945573793, 46496604627, 2330130198628, 118494430525573, 6096421370592533, 316645280669755956, 16576490090960754263, 873571148975832074915, 46298964043875792395392, 2465912665088397543706509, 131900710343673817734601975, 7082026383236714350731260152, 381526151282177147429713579019, 20615427152924581647222068540319, 1116940488173516027160256057162574] SeqW(AtomicList2, 20); [7, 116, 2397, 54845, 1329644, 33464881, 864627351, 22776683200, 609024723535, 16478750543705, 450190397799036, 12397538372467109, 343712858468053319, 9584085091610235280, 268571959802603851989, 7558772037473679862681, 213548821612723752662596, 6053567963855857530305675, 172122223664458866543268605, 4907277770241720608057395514] SeqW(AtomicList3, 20); [0, 6, 12, 90, 360, 2040, 10080, 54810, 290640, 1588356, 8676360, 47977776, 266378112, 1488801600, 8355739392, 47104393050, 266482019232, 1512589408044, 8610448069080, 49144928795820] SeqW(AtomicList4, 20); [0, 0, 0, 6, 0, 12, 0, 90, 0, 360, 0, 2040, 0, 10080, 0, 54810, 0, 290640, 0, 1588356] SeqW(AtomicList5, 20); [7, 248, 11380, 560089, 29125351, 1569958128, 86788339340, 4888825879881, 279426677977031, 16157131667825848, 943111939336618632, 55484322315357923295, 3285892503171164775331, 195702284602101274293904, 11712934523286758880149936, 704033995863342702374989573, 42477455605755398896927508851, 2571440107359622413265590226942, 156132324067001479278797740575360, 9505535222065315340412164983124315] SeqW(AtomicList6, 20); [0, 6, 0, 90, 0, 1680, 0, 34650, 0, 756756, 0, 17153136, 0, 399072960, 0, 9465511770, 0, 227873431500, 0, 5550996791340] SeqW(AtomicList7, 20); [1, 7, 25, 151, 751, 4411, 24697, 146455, 862351, 5195257, 31392967, 191815339, 1177508515, 7276161907, 45154764025, 281492498455, 1761076827895, 11055132835705, 69600761349175, 439370198255401] SeqW(AtomicList8, 20); [0, 6, 0, 222, 0, 8280, 0, 347850, 0, 15381828, 0, 705379416, 0, 33176670912, 0, 1590179139450, 0, 77338582832940, 0, 3805317108650772] SeqW(AtomicList9, 20); [0, 0, 0, 12, 0, 0, 0, 900, 0, 0, 0, 124320, 0, 0, 0, 20404692, 0, 0, 0, 3565834272] SeqW(AtomicList10, 20); [6, 222, 9918, 486924, 25267236, 1359631776, 75059524392, 4223303759148, 241144782230124, 13930829740017132, 812470444305924300, 47760356825349969600, 2826309951801018736800, 168207011284961649886800, 10060178088232285063542768, 604273284101165691102038556, 36433815687062371121118895932, 2204115927361189776716760043788, 133741833572484171893205858917004, 8137131251684373450885494321993544] SeqW(AtomicList11, 20); [7, 248, 11380, 577124, 30970588, 1724240804, 98508192580, 5736813639188, 339068764626556, 20277072462706100, 1224258843324348388, 74504869395134442884, 4564559749008113090620, 281250580532881468554692, 17415330397418786646707236, 1083032227236864061959662324, 67608117114236558395225328668, 4234657967432650999297571251028, 266038105281084969719145296706820, 16758805138961537889693234111512804] #Good paths (x>=y>=z): SeqGW(AtomicList1, 20); [2, 20, 328, 7480, 203176, 6211182, 206714074, 7336899407, 273892391945, 10649307342741, 428172896101165, 17705872314493431, 749878571241157489, 32418826689694348416, 1426841638137112004717, 63793830459393076747667, 2892158020340582449887009, 132754664924043492708227013, 6161798967035543718962532610, 288883222283520707614746820731] SeqGW(AtomicList2, 20); [2, 11, 94, 1102, 15555, 248239, 4324125, 80451430, 1575855961, 32170583918, 679454086275, 14764207771916, 328660778213440, 7469735592973418, 172863516984646383, 4064255876703426163, 96904549652068261697, 2339531574588039426453, 57118224184387094924409, 1408652232800360284464616] SeqGW(AtomicList3, 20); [0, 1, 0, 4, 4, 31, 76, 376, 1332, 5994, 24828, 112016, 500044, 2313815, 10787288, 51270984, 246265136, 1198208064, 5887369312, 29212675530] SeqGW(AtomicList4, 20); [0, 0, 0, 1, 0, 0, 0, 4, 0, 4, 0, 31, 0, 76, 0, 376, 0, 1332, 0, 5994] SeqGW(AtomicList5, 20); [2, 20, 392, 10076, 308794, 10635713, 398441947, 15910609458, 668028916680, 29206855477312, 1320278973721984, 61376155938006849, 2921956330642160652, 141988546015907480399, 7023987411657638359608, 352956796641795342983912, 17983988432058939859228520, 927734228865395980435400669, 48392903645851368612470472981, 2549699038949640998393766990510] SeqGW(AtomicList6, 20); [0, 1, 0, 5, 0, 42, 0, 462, 0, 6006, 0, 87516, 0, 1385670, 0, 23371634, 0, 414315330, 0, 7646001090] SeqGW(AtomicList7, 20); [1, 2, 5, 16, 56, 218, 897, 3907, 17677, 82864, 399191, 1970684, 9928426, 50931050, 265381781, 1402206785, 7500986535, 40574241582, 221679865651, 1222204655828] SeqGW(AtomicList8, 20); [0, 1, 0, 14, 0, 227, 0, 5095, 0, 133766, 0, 3939013, 0, 125968801, 0, 4290568003, 0, 153574639342, 0, 5721989787415] SeqGW(AtomicList9, 20); [0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 368, 0, 0, 0, 30305, 0, 0, 0, 2914078] SeqGW(AtomicList10, 20); [1, 14, 290, 7680, 238636, 8285506, 312077474, 12509563082, 526701471002, 23076216957520, 1044813920439200, 48630132961189400, 2317337976558074760, 112689430179458971738, 5577655817793682738378, 280392321290875174774106, 14290804691034216155457274, 737358053224726791171696484, 38466750733305875547325871500, 2026804534563403933416013171400] SeqGW(AtomicList11, 20); [2, 20, 392, 10488, 333672, 11915064, 462573560, 19135907480, 832159886696, 37676976167000, 1763538013533560, 84880305935069240, 4183482363310076776, 210450327205027977976, 10776850983863330674936, 560563642769633254378072, 29564515033467565424401000, 1578621550168522539513161752, 85230672941773727794765758840, 4647875122898490798606567265272]