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%I #4 Jul 25 2018 11:11:43
%S 1,2,2,3,5,3,5,7,7,5,8,17,10,17,8,13,35,21,21,35,13,21,61,46,74,46,61,
%T 21,34,127,91,158,158,91,127,34,55,265,186,440,718,440,186,265,55,89,
%U 507,409,1220,1964,1964,1220,409,507,89,144,1013,892,3655,6645,7477,6645
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4, 6, 7 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
%C ..2...5...7....17.....35.....61.....127.......265........507........1013
%C ..3...7..10....21.....46.....91.....186.......409........892........1931
%C ..5..17..21....74....158....440....1220......3655......10907.......33353
%C ..8..35..46...158....718...1964....6645.....27514.....103293......402198
%C .13..61..91...440...1964...7477...33695....166051.....806730.....4131259
%C .21.127.186..1220...6645..33695..219131...1493369....9934644....70625395
%C .34.265.409..3655..27514.166051.1493369..13595141..120265219..1153409542
%C .55.507.892.10907.103293.806730.9934644.120265219.1430955986.18455258095
%H R. H. Hardin, <a href="/A317266/b317266.txt">Table of n, a(n) for n = 1..199</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2)
%F k=2: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) -4*a(n-4) for n>5
%F k=3: [order 16]
%F k=4: [order 67] for n>68
%e Some solutions for n=5 k=4
%e ..0..0..0..0. .0..0..0..0. .0..0..1..1. .0..0..0..1. .0..1..1..0
%e ..0..1..0..0. .0..0..1..0. .0..1..1..1. .0..0..0..0. .0..0..0..0
%e ..1..1..0..1. .0..0..0..0. .1..1..1..1. .0..0..0..0. .0..0..1..1
%e ..1..1..1..1. .0..0..0..0. .1..1..1..1. .0..1..0..0. .0..0..0..1
%e ..1..1..1..1. .0..0..0..0. .1..1..1..0. .1..1..0..1. .0..0..0..0
%Y Column 1 is A000045(n+1).
%Y Column 2 is A303802.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Jul 25 2018
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