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%I #4 Apr 10 2018 19:13:13
%S 1,2,2,4,8,4,8,17,25,8,16,37,25,81,16,32,78,45,71,264,32,64,169,79,
%T 130,191,857,64,128,361,146,251,367,498,2785,128,256,778,286,497,896,
%U 917,1321,9050,256,512,1673,563,1051,2229,2669,2533,3505,29407,512,1024,3605
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
%C Table starts
%C ...1.....2....4.....8....16.....32......64......128.......256........512
%C ...2.....8...17....37....78....169.....361......778......1673.......3605
%C ...4....25...25....45....79....146.....286......563......1114.......2222
%C ...8....81...71...130...251....497....1051.....2274......4999......10972
%C ..16...264..191...367...896...2229....5771....15303.....41564.....113363
%C ..32...857..498...917..2669...9015...30536...106951....390471....1418770
%C ..64..2785.1321..2533..8283..36510..159831...722300...3485735...16654024
%C .128..9050.3505..6871.25770.150072..851266..5004858..32283797..204853561
%C .256.29407.9240.18334.79047.606756.4471550.34111427.294788397.2490596189
%H R. H. Hardin, <a href="/A302623/b302623.txt">Table of n, a(n) for n = 1..449</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4)
%F k=3: [order 9] for n>11
%F k=4: [order 8] for n>10
%F k=5: [order 15] for n>20
%F k=6: [order 21] for n>27
%F k=7: [order 35] for n>43
%F Empirical for row n:
%F n=1: a(n) = 2*a(n-1)
%F n=2: a(n) = 3*a(n-1) +a(n-2) -6*a(n-3) -2*a(n-4) +4*a(n-5) for n>6
%F n=3: a(n) = 2*a(n-1) +a(n-3) -2*a(n-4) for n>8
%F n=4: [order 8] for n>11
%F n=5: [order 16] for n>21
%F n=6: [order 29] for n>35
%F n=7: [order 51] for n>62
%e Some solutions for n=5 k=4
%e ..0..0..1..1. .0..1..1..0. .0..1..0..1. .0..0..1..0. .0..1..0..0
%e ..1..0..1..0. .0..0..1..0. .0..1..0..1. .1..0..1..0. .1..1..0..1
%e ..1..0..1..0. .1..0..1..0. .0..1..1..1. .1..0..1..0. .1..0..0..1
%e ..0..1..0..1. .0..0..1..1. .0..1..0..1. .1..1..1..0. .1..0..1..1
%e ..0..1..0..1. .1..1..0..0. .0..1..0..1. .1..0..1..1. .0..0..1..0
%Y Column 1 is A000079(n-1).
%Y Column 2 is A240478.
%Y Row 1 is A000079(n-1).
%Y Row 2 is A281470.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Apr 10 2018
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