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%I #4 Mar 08 2018 12:34:52
%S 0,1,1,1,3,1,2,11,11,2,3,37,71,37,3,5,129,450,450,129,5,8,450,2879,
%T 5232,2879,450,8,13,1568,18365,61561,61561,18365,1568,13,21,5464,
%U 117146,724165,1338834,724165,117146,5464,21,34,19041,747252,8514930,29114990
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
%C Table starts
%C ..0.....1.......1..........2............3..............5.................8
%C ..1.....3......11.........37..........129............450..............1568
%C ..1....11......71........450.........2879..........18365............117146
%C ..2....37.....450.......5232........61561.........724165...........8514930
%C ..3...129....2879......61561......1338834.......29114990.........632777378
%C ..5...450...18365.....724165.....29114990.....1170734982.......47042626155
%C ..8..1568..117146....8514930....632777378....47042626155.....3494400946777
%C .13..5464..747252..100122064..13752553340..1890308500802...259582877324570
%C .21.19041.4766519.1177281510.298894998879.75958861124241.19283328543117575
%H R. H. Hardin, <a href="/A300546/b300546.txt">Table of n, a(n) for n = 1..219</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2)
%F k=2: a(n) = 4*a(n-1) -2*a(n-2) +a(n-3) -a(n-4) for n>5
%F k=3: [order 8] for n>10
%F k=4: [order 41] for n>42
%e Some solutions for n=5 k=4
%e ..0..1..1..1. .0..1..1..0. .0..0..1..0. .0..0..1..0. .0..0..0..1
%e ..0..1..0..0. .0..1..1..0. .0..1..0..1. .1..1..0..1. .1..1..0..1
%e ..1..1..0..1. .1..0..0..0. .1..0..1..0. .0..1..1..1. .1..0..1..1
%e ..0..0..1..1. .0..1..0..0. .0..1..0..1. .0..0..0..0. .0..0..0..1
%e ..0..0..1..1. .0..1..1..0. .0..1..1..1. .1..1..1..1. .1..1..0..0
%Y Column 1 is A000045(n-1).
%Y Column 2 is A232031(n-1).
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Mar 08 2018
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