A284449
Number of n X 1 0..1 arrays with the number of 1's king-move adjacent to some 0 one less than the number of 0's adjacent to some 1.
Original entry on oeis.org
0, 0, 0, 1, 2, 6, 12, 28, 56, 119, 236, 481, 950, 1902, 3752, 7450, 14684, 29032, 57192, 112850, 222308, 438359, 863808, 1703239, 3357766, 6622471, 13061980, 25772503, 50859826, 100399602, 198235896, 391523612, 773453896, 1528361734, 3020781528, 5971996960
Offset: 0
Both solutions for n=4
..0. .0
..1. .0
..0. .1
..0. .0
-
a:= proc(n) option remember; `if`(n<6, [0$3, 1, 2, 6][n+1],
((n+2)*(5*n^4-98*n^3+661*n^2-1680*n+1164) *a(n-1)
-4*(2*n^5-37*n^4+226*n^3-442*n^2-87*n+204) *a(n-2)
-2*(3*n^4-63*n^3+376*n^2-468*n+264) *a(n-3)
+2*(8*n^5-155*n^4+1060*n^3-3035*n^2+3738*n-1752) *a(n-4)
-4*(5*n^5-101*n^4+750*n^3-2450*n^2+3312*n-1248) *a(n-5)
+4*(2*n-9)*(n^4-16*n^3+85*n^2-150*n+48) *a(n-6)) /
((n+3)*(n^4-20*n^3+139*n^2-372*n+300)))
end:
seq(a(n), n=0..35); # Alois P. Heinz, Apr 23 2018
A284450
Number of n X 3 0..1 arrays with the number of 1's king-move adjacent to some 0 one less than the number of 0's adjacent to some 1.
Original entry on oeis.org
1, 0, 102, 250, 5253, 16478, 278315, 1019120, 15188955, 62846854, 850526529, 3891052774, 48586797398, 241642747938, 2818541243728, 15034216343154, 165507316465985, 936470483789652, 9815405179117090, 58379693308010828
Offset: 1
Some solutions for n=4
..0..0..1. .0..1..0. .1..0..1. .1..0..0. .1..0..1. .0..0..0. .0..1..1
..1..0..1. .0..0..1. .0..0..1. .1..1..1. .1..0..1. .0..0..1. .0..1..1
..1..0..0. .0..1..1. .1..0..0. .1..0..0. .0..0..0. .1..1..1. .0..1..0
..1..0..0. .0..1..1. .1..0..0. .0..0..0. .1..0..0. .1..0..0. .1..0..0
A284451
Number of n X 4 0..1 arrays with the number of 1's king-move adjacent to some 0 one less than the number of 0's adjacent to some 1.
Original entry on oeis.org
2, 0, 250, 3384, 54248, 824052, 12957944, 203401448, 3209101642, 50702668880, 801990075576, 12692871462160, 200953195066764, 3182000912440584, 50388819126999402, 797940889459632096, 12635596604122356028
Offset: 1
Some solutions for n=4
..1..1..0..0. .0..0..1..1. .1..0..1..0. .0..1..1..1. .1..0..0..1
..0..0..0..0. .0..0..1..0. .0..1..0..1. .0..1..1..0. .1..0..0..0
..1..1..0..1. .0..1..0..1. .1..0..0..0. .0..0..0..1. .1..1..0..0
..0..0..1..1. .1..0..0..1. .1..1..0..0. .0..0..1..0. .1..1..1..0
A284452
Number of n X 5 0..1 arrays with the number of 1's king-move adjacent to some 0 one less than the number of 0's adjacent to some 1.
Original entry on oeis.org
6, 0, 5253, 54248, 4190874, 52793160, 3478866516, 51105257464, 3013637890236, 50103215952170, 2690074942950538, 49496986589768228, 2453145792485211975, 49093699484421451316, 2273291621866265836761, 48802745578218591419362
Offset: 1
Some solutions for n=4
..0..0..1..1..0. .0..0..1..1..0. .0..1..0..1..1. .1..1..1..0..0
..0..1..0..0..1. .0..0..0..1..1. .0..0..0..0..0. .0..0..0..0..0
..0..1..1..0..0. .1..1..0..0..1. .1..1..0..1..1. .0..1..0..1..1
..1..1..1..0..0. .0..0..1..0..1. .0..0..1..1..1. .1..0..1..1..0
A284453
Number of n X 6 0..1 arrays with the number of 1's king-move adjacent to some 0 one less than the number of 0's adjacent to some 1.
Original entry on oeis.org
12, 0, 16478, 824052, 52793160, 3177012844, 197373621124, 12262301470824, 765844185617960, 47948372703291720, 3007592277730507060, 188906442508764876656, 11876939646231731080510, 747292579695048713129724
Offset: 1
Some solutions for n=3
..1..1..1..0..0..0. .1..1..1..0..0..1. .1..0..1..0..1..0. .1..0..1..0..0..0
..1..1..0..1..1..0. .1..1..0..0..0..0. .0..0..1..1..0..0. .1..1..1..1..0..0
..1..0..0..0..0..1. .1..0..0..1..0..1. .1..1..0..1..0..0. .1..0..0..0..0..1
A284454
Number of n X 7 0..1 arrays with the number of 1's king-move adjacent to some 0 one less than the number of 0's adjacent to some 1.
Original entry on oeis.org
28, 0, 278315, 12957944, 3478866516, 197373621124, 45913351929099, 3020610942888634, 635171432700031740, 46935468157115829048, 9070472121517777538083, 735727339860385496580626
Offset: 1
Some solutions for n=3
..0..1..1..0..1..1..0. .0..1..0..0..0..0..1. .0..0..1..0..1..0..1
..0..1..0..0..0..1..0. .0..1..1..1..0..0..1. .0..1..0..1..0..0..0
..1..0..1..0..0..1..1. .0..1..1..0..0..1..1. .1..1..1..1..0..0..0
A284448
Number of n X n 0..1 arrays with the number of 1's king-move adjacent to some 0 one less than the number of 0's adjacent to some 1.
Original entry on oeis.org
0, 0, 102, 3384, 4190874, 3177012844, 45913351929099, 746140228341333064, 140666601117969492988244
Offset: 1
Some solutions for n=4
..1..1..0..0. .1..1..0..0. .0..1..0..0. .0..0..1..0. .0..0..0..0
..0..0..0..1. .1..1..1..0. .0..1..1..1. .0..1..0..0. .0..1..1..0
..1..1..0..0. .1..0..0..0. .0..0..1..0. .1..1..0..1. .1..1..0..0
..1..1..0..1. .0..1..0..1. .0..0..1..1. .1..1..0..1. .1..1..1..1
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