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A303102 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%I A303102 #4 Apr 18 2018 12:39:07
%S A303102 0,1,0,1,3,0,2,15,11,0,3,46,77,34,0,5,161,431,486,111,0,8,601,2913,
%T A303102 4667,2869,361,0,13,2208,19393,58160,49534,17229,1172,0,21,8053,
%U A303102 128921,709333,1138331,523578,102952,3809,0,34,29415,857789,8650205,25372284,22292709
%N A303102 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
%C A303102 Table starts
%C A303102 .0.....1.......1.........2............3..............5.................8
%C A303102 .0.....3......15........46..........161............601..............2208
%C A303102 .0....11......77.......431.........2913..........19393............128921
%C A303102 .0....34.....486......4667........58160.........709333...........8650205
%C A303102 .0...111....2869.....49534......1138331.......25372284.........568099880
%C A303102 .0...361...17229....523578.....22292709......906385523.......37220475492
%C A303102 .0..1172..102952...5550469....436394066....32409609245.....2441756629583
%C A303102 .0..3809..616065..58797885...8545589681..1158734336743...160164698180399
%C A303102 .0.12377.3685099.622939052.167325743073.41428642572259.10505922762123798
%H A303102 R. H. Hardin, <a href="/A303102/b303102.txt">Table of n, a(n) for n = 1..180</a>
%F A303102 Empirical for column k:
%F A303102 k=1: a(n) = a(n-1)
%F A303102 k=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4)
%F A303102 k=3: [order 11]
%F A303102 k=4: [order 26]
%F A303102 k=5: [order 90] for n>91
%F A303102 Empirical for row n:
%F A303102 n=1: a(n) = a(n-1) +a(n-2)
%F A303102 n=2: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3) +4*a(n-4) for n>5
%F A303102 n=3: [order 14] for n>15
%F A303102 n=4: [order 42] for n>43
%e A303102 Some solutions for n=5 k=4
%e A303102 ..0..1..1..1. .0..0..1..1. .0..0..1..1. .0..0..0..0. .0..1..0..1
%e A303102 ..1..0..1..0. .1..1..1..1. .1..1..0..0. .0..1..1..1. .0..0..1..0
%e A303102 ..1..0..0..1. .0..0..0..1. .1..1..1..1. .0..0..1..0. .1..0..0..0
%e A303102 ..0..1..1..0. .0..1..1..0. .0..0..0..0. .0..1..0..1. .0..1..1..1
%e A303102 ..1..1..0..0. .1..1..0..0. .1..1..1..1. .1..0..1..0. .1..0..0..0
%Y A303102 Column 2 is A180762.
%Y A303102 Row 1 is A000045(n-1).
%Y A303102 Row 2 is A232077(n-1).
%K A303102 nonn,tabl
%O A303102 1,5
%A A303102 _R. H. Hardin_, Apr 18 2018