A068265
1/15 the number of colorings of an n X n square array with 15 colors.
Original entry on oeis.org
1, 2562, 1121513134, 83883341208384732, 1071996076636962150571633386, 2340759471154169773945494478241264553960, 873306114650864371018759651512626175923988398193371716, 55670142239312854542084127479622099015674204276236803402441613218850844
Offset: 1
A068266
1/16 the number of colorings of an n X n square array with 16 colors.
Original entry on oeis.org
1, 3165, 1982119455, 245622604880564955, 6022672393066051875922651155, 29220829891835424567142114269163936868895, 28052931461360411640129365206060753190589761972840149815, 5329007775881376959796836954274567596610268811025721999774999394622215355
Offset: 1
A068267
1/17 the number of colorings of an n X n square array with 17 colors.
Original entry on oeis.org
1, 3856, 3373402576, 669566077899139456, 30151771791510037597255660816, 308053647651282803104693654675496996201056, 714058835879284684324470416584413995932326192121670240896, 375522326791659350740130359662485880296223549591107434149113597657567050816
Offset: 1
A068268
1/18 the number of colorings of an n X n square array with 18 colors.
Original entry on oeis.org
1, 4641, 5554571857, 1714419367669298289, 136461767759964622690609683537, 2801124263786734144622842493797034683405617, 14827953377838619886793709359009173477911476430325930106481, 20242190237452646688395985657256161903754274932459524235140863308223305109841
Offset: 1
A068269
1/19 the number of colorings of an n X n square array with 19 colors.
Original entry on oeis.org
1, 5526, 8882874018, 4153630571837864748, 564981170863476314096512687566, 22354853275061169487985050625489956484533056, 257300965334378745090532920060644632998190650709754736514068, 861475141050998806961235302195978945049151803599433480523424276423626596675468
Offset: 1
A068270
1/20 the number of colorings of an n X n square array with 20 colors.
Original entry on oeis.org
1, 6517, 13841287219, 9580458187250990407, 2161111220298293067819628379911, 158872597397775739573835110149847235229271675, 3806290340846629510463844992746098005507806101928649895595171, 29719114772241665792629546781476756531800106771541628945462624575440369135473679
Offset: 1
A277443
Square array A(n,k) (n>=1, k>=1) read by antidiagonals: A(n,k) is the number of n-colorings of the prism graph Y_k on 2k vertices.
Original entry on oeis.org
0, 0, 0, 0, 2, 0, 0, 0, 18, 0, 0, 2, 12, 84, 0, 0, 0, 114, 264, 260, 0, 0, 2, 180, 2652, 1920, 630, 0, 0, 0, 858, 16080, 29660, 8520, 1302, 0, 0, 2, 1932, 119844, 367080, 198030, 28140, 2408, 0, 0, 0, 7074, 816984, 4843460, 4067280, 932862, 76272, 4104, 0, 0, 2, 18660, 5784492, 62682480, 85847910, 28576380, 3440024, 179424, 6570, 0
Offset: 1
Square array A(n,k) begins:
0, 0, 0, 0, 0, 0, 0, ...
0, 2, 0, 2, 0, 2, 0, ...
0, 18, 12, 114, 180, 858, 1932, ...
0, 84, 264, 2652, 16080, 119844, 816984, ...
0, 260, 1920, 29660, 367080, 4843460, 62682480, ...
0, 630, 8520, 198030, 4067280, 85847910, 1800687000, ...
Cf.
A277444 (colorings of Möbius ladders),
A182406 (square grid graphs).
A277444
Square array A(n,k) (n>=1, k>=1) read by antidiagonals: A(n,k) is the number of n-colorings of the Möbius ladder M_k on 2k vertices.
Original entry on oeis.org
0, 0, 2, 0, 0, 6, 0, 2, 0, 12, 0, 0, 42, 24, 20, 0, 2, 48, 420, 120, 30, 0, 0, 306, 2160, 2420, 360, 42, 0, 2, 600, 17532, 27600, 9750, 840, 56, 0, 0, 2442, 115464, 375260, 191760, 30702, 1680, 72, 0, 2, 6048, 830100, 4810680, 4098510, 917280, 81032, 3024, 90, 0, 0, 20706, 5745120, 62813540, 85691640, 28669662, 3406368, 187560, 5040, 110
Offset: 1
Square array A(n,k) begins:
0, 0, 0, 0, 0, 0, 0, ...
2, 0, 2, 0, 2, 0, 2, ...
6, 0, 42, 48, 306, 600, 2442, ...
12, 24, 420, 2160, 17532, 115464, 830100, ...
20, 120, 2420, 27600, 375260, 4810680, 62813540, ...
30, 360, 9750, 191760, 4098510, 85691640, 1801468230, ...
Cf.
A277443 (colorings of prism graphs),
A182406 (square grid graphs).
Comments