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%I #6 May 24 2021 15:02:10
%S 0,1,1,1,4,1,2,18,18,2,3,64,129,64,3,5,236,899,899,236,5,8,888,6205,
%T 11179,6205,888,8,13,3336,43066,143548,143548,43066,3336,13,21,12512,
%U 298361,1850266,3426869,1850266,298361,12512,21,34,46928,2068149
%N T(n,k) = Number of n X k 0..1 arrays with every element equal to 1, 2, 3, 4, 5 or 7 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ..0.....1........1..........2.............3...............5.................8
%C ..1.....4.......18.........64...........236.............888..............3336
%C ..1....18......129........899..........6205...........43066............298361
%C ..2....64......899......11179........143548.........1850266..........23808476
%C ..3...236.....6205.....143548.......3426869........81988764........1958821107
%C ..5...888....43066....1850266......81988764......3643124959......161617794805
%C ..8..3336...298361...23808476....1958821107....161617794805....13311860331263
%C .13.12512..2068149..306389599...46801360032...7170422794173..1096571119921011
%C .21.46928.14334327.3942948157.1118229413140.318133492126048.90332592148780928
%H R. H. Hardin, <a href="/A299142/b299142.txt">Table of n, a(n) for n = 1..180</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2).
%F k=2: a(n) = 4*a(n-1) -2*a(n-2) +4*a(n-3) for n>4.
%F k=3: [order 10] for n>11.
%F k=4: [order 33] for n>34.
%e Some solutions for n=5, k=4
%e ..0..0..1..0. .0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..0..0
%e ..1..0..0..1. .0..1..0..0. .1..1..1..0. .0..0..1..0. .0..1..0..1
%e ..0..1..0..1. .0..1..1..0. .0..0..0..1. .0..0..0..1. .1..0..1..0
%e ..0..1..0..0. .0..0..1..1. .0..0..1..0. .1..1..0..1. .0..1..0..1
%e ..0..1..1..1. .0..0..0..1. .1..1..0..0. .1..0..0..1. .1..0..0..0
%Y Column 1 is A000045(n-1).
%Y Column 2 is A231950(n-1).
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Feb 03 2018
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