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A303084 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%I A303084 #4 Apr 18 2018 12:21:10
%S A303084 1,1,2,1,2,4,1,12,2,8,1,20,32,3,16,1,72,29,112,6,32,1,168,258,90,416,
%T A303084 10,64,1,496,432,1455,304,1512,21,128,1,1296,2525,3667,11767,1054,
%U A303084 5472,42,256,1,3616,6313,33152,34430,84474,4182,19904,86,512,1,9760,30188,157838
%N A303084 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
%C A303084 Table starts
%C A303084 ...1..1.....1.....1........1.........1............1.............1
%C A303084 ...2..2....12....20.......72.......168..........496..........1296
%C A303084 ...4..2....32....29......258.......432.........2525..........6313
%C A303084 ...8..3...112....90.....1455......3667........33152........157838
%C A303084 ..16..6...416...304....11767.....34430.......636070.......4585419
%C A303084 ..32.10..1512..1054....84474....409478.....13375327.....170974652
%C A303084 ..64.21..5472..4182...615471...4862916....266882021....5924274499
%C A303084 .128.42.19904.17369..4647197..60442630...5754725245..218955384065
%C A303084 .256.86.72396.75377.35089147.764631608.125608726910.8100166904419
%H A303084 R. H. Hardin, <a href="/A303084/b303084.txt">Table of n, a(n) for n = 1..180</a>
%F A303084 Empirical for column k:
%F A303084 k=1: a(n) = 2*a(n-1)
%F A303084 k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
%F A303084 k=3: [order 11]
%F A303084 k=4: [order 56] for n>57
%F A303084 Empirical for row n:
%F A303084 n=1: a(n) = a(n-1)
%F A303084 n=2: a(n) = 2*a(n-1) +4*a(n-2) -4*a(n-3) -4*a(n-4)
%F A303084 n=3: [order 17] for n>18
%F A303084 n=4: [order 67] for n>68
%e A303084 Some solutions for n=5 k=4
%e A303084 ..0..0..0..1. .0..1..1..1. .0..0..1..1. .0..1..1..1. .0..0..0..1
%e A303084 ..0..0..0..1. .1..1..1..1. .0..0..1..1. .1..1..1..1. .1..0..0..1
%e A303084 ..0..1..0..1. .0..0..0..0. .1..0..0..0. .0..1..0..1. .1..0..0..1
%e A303084 ..0..0..0..0. .0..0..0..0. .1..0..0..1. .1..1..1..1. .0..0..0..1
%e A303084 ..0..0..0..1. .0..0..0..0. .0..0..0..1. .0..1..1..1. .1..0..0..1
%Y A303084 Column 1 is A000079(n-1).
%Y A303084 Column 2 is A240513(n-2).
%Y A303084 Row 2 is A302368.
%K A303084 nonn,tabl
%O A303084 1,3
%A A303084 _R. H. Hardin_, Apr 18 2018