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%I #4 Feb 10 2018 10:30:49
%S 1,2,2,3,4,3,5,4,4,5,8,8,1,8,8,13,32,4,4,32,13,21,32,10,21,10,32,21,
%T 34,64,6,32,32,6,64,34,55,256,11,36,231,36,11,256,55,89,256,41,161,
%U 163,163,161,41,256,89,144,512,24,264,546,211,546,264,24,512,144,233,2048,42,430
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 5, 6 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ..1...2..3...5....8...13....21.....34.....55......89......144.......233
%C ..2...4..4...8...32...32....64....256....256.....512.....2048......2048
%C ..3...4..1...4...10....6....11.....41.....24......42......169.......100
%C ..5...8..4..21...32...36...161....264....430....1475.....2598......4872
%C ..8..32.10..32..231..163...546...2904...2321....8729....37095.....34873
%C .13..32..6..36..163..211...804...3138...4869...21921....69029....124071
%C .21..64.11.161..546..804..6326..19745..39495..290364...855008...2191987
%C .34.256.41.264.2904.3138.19745.174794.205522.1778833.11489465..16992517
%C .55.256.24.430.2321.4869.39495.205522.665961.5936888.26103440.114805573
%H R. H. Hardin, <a href="/A299451/b299451.txt">Table of n, a(n) for n = 1..241</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2)
%F k=2: a(n) = 8*a(n-3) for n>4
%F k=3: [order 18] for n>19
%F k=4: [order 62] for n>63
%e Some solutions for n=5 k=4
%e ..0..1..0..0. .0..0..1..1. .0..1..1..0. .0..0..0..1. .0..1..1..0
%e ..1..1..1..1. .0..0..1..1. .1..0..1..1. .0..0..0..1. .0..1..1..0
%e ..0..1..1..1. .0..0..0..0. .1..1..1..0. .1..1..0..0. .1..1..1..1
%e ..1..1..0..0. .1..1..0..0. .0..1..1..1. .0..0..0..1. .1..0..0..1
%e ..0..1..1..1. .1..1..0..0. .1..0..1..0. .0..0..0..1. .1..0..0..1
%Y Column 1 is A000045(n+1).
%Y Column 2 is A096252(n-1).
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Feb 10 2018
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