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A303040 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%I A303040 #4 Apr 17 2018 13:23:44
%S A303040 1,2,2,3,3,4,5,11,6,8,8,21,14,10,16,13,31,28,35,21,32,21,113,56,74,71,
%T A303040 42,64,34,363,150,234,197,186,86,128,55,813,360,869,703,544,459,179,
%U A303040 256,89,1751,828,2926,3069,2494,1686,1287,370,512,144,5001,1906,8500,11079
%N A303040 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
%C A303040 Table starts
%C A303040 ...1...2....3.....5......8......13.......21........34.........55..........89
%C A303040 ...2...3...11....21.....31.....113......363.......813.......1751........5001
%C A303040 ...4...6...14....28.....56.....150......360.......828.......1906........4628
%C A303040 ...8..10...35....74....234.....869.....2926......8500......27931.......96592
%C A303040 ..16..21...71...197....703....3069....11079.....39281.....147655......574771
%C A303040 ..32..42..186...544...2494...13597....59654....251705....1186522.....5869222
%C A303040 ..64..86..459..1686...9882...63254...345668...1853428...10924077....67726475
%C A303040 .128.179.1287..5252..38855..298328..2060154..13840842..103929273...827923879
%C A303040 .256.370.3490.16336.158630.1487003.13122422.112389422.1107624272.11716920536
%H A303040 R. H. Hardin, <a href="/A303040/b303040.txt">Table of n, a(n) for n = 1..219</a>
%F A303040 Empirical for column k:
%F A303040 k=1: a(n) = 2*a(n-1)
%F A303040 k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
%F A303040 k=3: [order 13] for n>16
%F A303040 k=4: [order 70]
%F A303040 Empirical for row n:
%F A303040 n=1: a(n) = a(n-1) +a(n-2)
%F A303040 n=2: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) +12*a(n-4) -16*a(n-5) for n>6
%F A303040 n=3: [order 11] for n>12
%F A303040 n=4: [order 61] for n>62
%e A303040 Some solutions for n=5 k=4
%e A303040 ..0..1..1..0. .0..1..0..1. .0..1..0..1. .0..0..0..1. .0..1..0..1
%e A303040 ..0..0..0..0. .1..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..0
%e A303040 ..0..1..1..1. .0..1..0..1. .0..1..0..1. .0..1..1..1. .1..1..0..1
%e A303040 ..0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1
%e A303040 ..0..1..0..1. .0..1..0..1. .1..0..0..1. .0..1..0..1. .0..0..0..1
%Y A303040 Column 1 is A000079(n-1).
%Y A303040 Column 2 is A240513.
%Y A303040 Row 1 is A000045(n+1).
%Y A303040 Row 2 is A302310.
%K A303040 nonn,tabl
%O A303040 1,2
%A A303040 _R. H. Hardin_, Apr 17 2018