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%I #4 Apr 15 2018 10:50:18
%S 1,1,2,1,2,4,1,12,2,8,1,20,37,3,16,1,72,53,141,6,32,1,168,197,238,569,
%T 10,64,1,496,818,2278,1102,2262,21,128,1,1296,2548,12782,20937,5570,
%U 8968,42,256,1,3616,10926,98458,200186,206332,28594,35667,86,512,1,9760,42671
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
%C Table starts
%C ...1..1......1......1.........1...........1.............1...............1
%C ...2..2.....12.....20........72.........168...........496............1296
%C ...4..2.....37.....53.......197.........818..........2548...........10926
%C ...8..3....141....238......2278.......12782.........98458..........714934
%C ..16..6....569...1102.....20937......200186.......2727690........37626360
%C ..32.10...2262...5570....206332.....3452246......89290791......2247650354
%C ..64.21...8968..28594...2059835....60501563....2899297652....133518102376
%C .128.42..35667.149206..20622709..1073161270...94799190457...7977498513759
%C .256.86.141839.788373.206851726.19073141368.3098646840396.476377988322833
%H R. H. Hardin, <a href="/A302889/b302889.txt">Table of n, a(n) for n = 1..180</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
%F k=3: [order 10]
%F k=4: [order 35] for n>37
%F Empirical for row n:
%F n=1: a(n) = a(n-1)
%F n=2: a(n) = 2*a(n-1) +4*a(n-2) -4*a(n-3) -4*a(n-4)
%F n=3: [order 16] for n>17
%F n=4: [order 51] for n>54
%e Some solutions for n=5 k=4
%e ..0..1..1..0. .0..1..1..1. .0..1..1..0. .0..0..0..0. .0..1..1..0
%e ..1..1..1..0. .1..1..1..0. .0..1..1..0. .1..0..0..1. .0..1..1..1
%e ..0..1..1..0. .0..1..1..0. .0..1..1..1. .1..0..0..1. .0..1..1..1
%e ..0..1..1..0. .0..1..1..1. .1..1..1..0. .0..0..0..0. .1..1..1..0
%e ..0..1..1..1. .0..1..1..0. .0..1..1..1. .0..0..0..1. .1..1..1..0
%Y Column 1 is A000079(n-1).
%Y Column 2 is A240513(n-2).
%Y Row 2 is A302368.
%K nonn,tabl
%O 1,3
%A _R. H. Hardin_, Apr 15 2018
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