The first 30 terms of the sequences enumerating  Rduced Generalized 3 by n La\

    tin Rectangles with respect to all subests of, {-1, 0, 1}



                              By Shalosh B. Ekhad





                                Prop. number, 1



The first, 30, terms, starting at n=1 of the number of 3-rowed matrices where\
     each row is a permutation of {1....,n}, the first  row is [1,...n]

and M[1,i]<>M[1,j], M[1,i]<>M[3,j], M[2,i]<>M[3,j] whenever j-i belongs to,

    {-1}, are



[2, 1, 6, 62, 1313, 42477, 1935760, 117400296, 9122732829, 882589173397, 
103948061916622, 14635864094630334, 2426899729335368021, 467989369843349186921,
103822170353311931786832, 26252306069242468482844576, 
7504692905943545775357234633, 2408077981273748373420949017081, 
861811655210061141574137090084358, 342044526905275709898556997886861838, 
149779902061637436054756427510250507289, 
72029324432809759007919356866951964576117, 
37880642592771808885078258631654250575821376, 
21702203550798931901926014126847856011874069160, 
13496904753756384109042031910490164829062334881925, 
9082304756068904745190987176059561023753951580491821, 
6593034732397262916279411844664155171842136550967651246, 
5148658537591534503332661525890783195564287163758099781806, 
4314198609617052205807603994795822432512075888015617908201197, 
3869531295644661261031525487651201139998799321393746987027320593]


                 ---------------------------------------------





                                Prop. number, 2



The first, 30, terms, starting at n=1 of the number of 3-rowed matrices where\
     each row is a permutation of {1....,n}, the first  row is [1,...n]

and M[1,i]<>M[1,j], M[1,i]<>M[3,j], M[2,i]<>M[3,j] whenever j-i belongs to, {0},

    are



[0, 0, 2, 24, 552, 21280, 1073760, 70299264, 5792853248, 587159944704, 
71822743499520, 10435273503677440, 1776780700509416448, 350461958856515690496,
79284041282622163140608, 20392765404792755583221760, 
5917934230798104348783083520, 1924427226324694427836833857536, 
696979289286274520909680184328192, 279603955400790511301713870268399616, 
123628789491780992885162936945243586560, 
59978391318683176126243015049924098129920, 
31797067318326418953118135360652301227261952, 
18351221543403106806973178855136356500120797184, 
11490247108618333261391185675249978428048940204032, 
7780327407929537088396311532286768756314104817254400, 
5680568961727056056439332473537950500726026396290252800, 
4459899698108740682204436081187213868321646434985248292864, 
3755729419902556177594011483711437582210320606428071637024768, 
3384313347969470506399197919009145163215859763380618974319345664]


                 ---------------------------------------------





                                Prop. number, 3



The first, 30, terms, starting at n=1 of the number of 3-rowed matrices where\
     each row is a permutation of {1....,n}, the first  row is [1,...n]

and M[1,i]<>M[1,j], M[1,i]<>M[3,j], M[2,i]<>M[3,j] whenever j-i belongs to, {1},

    are



[2, 1, 6, 62, 1313, 42477, 1935760, 117400296, 9122732829, 882589173397, 
103948061916622, 14635864094630334, 2426899729335368021, 467989369843349186921,
103822170353311931786832, 26252306069242468482844576, 
7504692905943545775357234633, 2408077981273748373420949017081, 
861811655210061141574137090084358, 342044526905275709898556997886861838, 
149779902061637436054756427510250507289, 
72029324432809759007919356866951964576117, 
37880642592771808885078258631654250575821376, 
21702203550798931901926014126847856011874069160, 
13496904753756384109042031910490164829062334881925, 
9082304756068904745190987176059561023753951580491821, 
6593034732397262916279411844664155171842136550967651246, 
5148658537591534503332661525890783195564287163758099781806, 
4314198609617052205807603994795822432512075888015617908201197, 
3869531295644661261031525487651201139998799321393746987027320593]


                 ---------------------------------------------





                                Prop. number, 4



The first, 30, terms, starting at n=1 of the number of 3-rowed matrices where\
     each row is a permutation of {1....,n}, the first  row is [1,...n]

and M[1,i]<>M[1,j], M[1,i]<>M[3,j], M[2,i]<>M[3,j] whenever j-i belongs to,

    {-1, 0}, are



[0, 0, 0, 1, 16, 626, 34793, 2448698, 212591901, 22410141583, 2826068083903, 
420706857462140, 73066048356158467, 14651039415160888971, 
3360765538132054881490, 874732223620153197921683, 256457329198752749650793242,
84144346846672777343534582494, 30715376137755742180387854986738, 
12408081283255508492222248166348699, 5520535192109691525910498789692014974, 
2693277069989852786991110986897525867812, 
1435034457905681942963517204363641046736891, 
832005700801799898295215530485341874817912044, 
523119199196870376401286535832186729870519273199, 
355570228565588036434264653221366083815504044143573, 
260519703286922515816299539234074573785317033822238713, 
205199293262703669476214313070010686874923587320282893438, 
173317074705315223321413623504457397740777284887096563742793, 
156610061723714331254638610831700327131987278418256175269652597]


                 ---------------------------------------------





                                Prop. number, 5



The first, 30, terms, starting at n=1 of the number of 3-rowed matrices where\
     each row is a permutation of {1....,n}, the first  row is [1,...n]

and M[1,i]<>M[1,j], M[1,i]<>M[3,j], M[2,i]<>M[3,j] whenever j-i belongs to,

    {-1, 1}, are



[2, 1, 4, 19, 201, 3991, 141600, 7535121, 544217321, 50331967349, 5753839331060
, 793452004739351, 129591285448882625, 24706656666823688235, 
5433133090818355069904, 1364319981333709113590421, 387848974756110764465703969,
123887281087143194183671172617, 44170952540387737246319649697444, 
17475998991273798003806337891276955, 7632366136264418356428791748325414201, 
3662106238349846640519611963013122782879, 
1922173984353773500674107966108571606417888, 
1099375585072036348452257972798698907687838265, 
682711317418290953848066590833043750833200258233, 
458815451904577175050892666275771033318265998086909, 
332684381381027338208659237246098376541288212316308724, 
259538780983005596182629908056895880272029463932510149887, 
217278769302654086790441669322937175965295238659214696374353, 
194726762903847969439384742965108084501466874460271388473878451]


                 ---------------------------------------------





                                Prop. number, 6



The first, 30, terms, starting at n=1 of the number of 3-rowed matrices where\
     each row is a permutation of {1....,n}, the first  row is [1,...n]

and M[1,i]<>M[1,j], M[1,i]<>M[3,j], M[2,i]<>M[3,j] whenever j-i belongs to,

    {0, 1}, are



[0, 0, 0, 1, 16, 626, 34793, 2448698, 212591901, 22410141583, 2826068083903, 
420706857462140, 73066048356158467, 14651039415160888971, 
3360765538132054881490, 874732223620153197921683, 256457329198752749650793242,
84144346846672777343534582494, 30715376137755742180387854986738, 
12408081283255508492222248166348699, 5520535192109691525910498789692014974, 
2693277069989852786991110986897525867812, 
1435034457905681942963517204363641046736891, 
832005700801799898295215530485341874817912044, 
523119199196870376401286535832186729870519273199, 
355570228565588036434264653221366083815504044143573, 
260519703286922515816299539234074573785317033822238713, 
205199293262703669476214313070010686874923587320282893438, 
173317074705315223321413623504457397740777284887096563742793, 
156610061723714331254638610831700327131987278418256175269652597]


                 ---------------------------------------------





                                Prop. number, 7



The first, 30, terms, starting at n=1 of the number of 3-rowed matrices where\
     each row is a permutation of {1....,n}, the first  row is [1,...n]

and M[1,i]<>M[1,j], M[1,i]<>M[3,j], M[2,i]<>M[3,j] whenever j-i belongs to,

    {-1, 0, 1}, are



[0, 0, 0, 0, 0, 4, 312, 28128, 3126568, 395167152, 56981282088, 9407962940912,
1774039799569368, 380353186069754448, 92229126464229063720, 
25155057733080402713040, 7675795571661419596354872, 
2606951068207408842918822800, 980742935952837296283921490920, 
406845627163459957280928553896336, 185323841960276422068586366083491384, 
92334527925732450281277382419019097040, 
50136323962500003423637011920356564859976, 
29568661928817902018736409334853795458398288, 
18881599049069057545497242269699612182509137752, 
13016789736563218417655682814607701982519316937488, 
9661443528936161860621038135668656195360676889740328, 
7700972979456371845289153914347999803632941787676068368, 
6576241492497267292153531978145563482096777562669369130616, 
6002970102288845217292166343372530348699597790130746783613264]


                 ---------------------------------------------



     This concludes this paper that took, 1070.909, seconds to generate .