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%I #4 Feb 23 2018 08:36:42
%S 0,1,1,1,4,1,2,17,17,2,3,61,113,61,3,5,216,628,628,216,5,8,793,3669,
%T 5663,3669,793,8,13,2907,21792,51862,51862,21792,2907,13,21,10622,
%U 128610,486305,766231,486305,128610,10622,21,34,38809,758715,4532025,11576060
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 4, 6, 7 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ..0.....1.......1.........2...........3.............5...............8
%C ..1.....4......17........61.........216...........793............2907
%C ..1....17.....113.......628........3669.........21792..........128610
%C ..2....61.....628......5663.......51862........486305.........4532025
%C ..3...216....3669.....51862......766231......11576060.......173419447
%C ..5...793...21792....486305....11576060.....281861630......6789384478
%C ..8..2907..128610...4532025...173419447....6789384478....262361247480
%C .13.10622..758715..42210111..2597671575..163627792463..10149632583491
%C .21.38809.4478515.393354513.38941599079.3947880819311.393165011518395
%H R. H. Hardin, <a href="/A300040/b300040.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) = 3*a(n-1) +a(n-2) +4*a(n-3) +4*a(n-4) for n>5
%F k=3: [order 14] for n>16
%F k=4: [order 49] for n>51
%e Some solutions for n=5 k=4
%e ..0..1..0..1. .0..1..1..0. .0..1..0..1. .0..0..0..1. .0..0..0..0
%e ..1..0..1..0. .1..0..1..0. .1..0..1..1. .1..0..1..0. .0..1..0..1
%e ..1..1..1..0. .0..1..0..0. .1..0..0..1. .1..0..1..0. .0..1..0..1
%e ..0..0..0..1. .1..0..1..1. .1..1..1..0. .1..0..1..1. .0..1..0..1
%e ..1..1..0..0. .0..0..1..1. .1..0..0..1. .0..1..0..1. .1..0..0..1
%Y Column 1 is A000045(n-1).
%Y Column 2 is A297917.
%Y Column 3 is A299223.
%Y Column 4 is A299224.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Feb 23 2018
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