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%I #4 Mar 05 2018 14:41:10
%S 0,1,1,1,3,1,2,10,10,2,3,30,53,30,3,5,96,272,272,96,5,8,307,1390,2227,
%T 1390,307,8,13,981,7179,18205,18205,7179,981,13,21,3137,37042,150352,
%U 240196,150352,37042,3137,21,34,10034,191135,1240541,3175101,3175101
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 3 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.....10.......30.........96..........307............981
%C ..1....10.....53......272.......1390.........7179..........37042
%C ..2....30....272.....2227......18205.......150352........1240541
%C ..3....96...1390....18205.....240196......3175101.......41940055
%C ..5...307...7179...150352....3175101.....67378450.....1429216222
%C ..8...981..37042..1240541...41940055...1429216222....48707694395
%C .13..3137.191135.10232500..553858752..30305915964..1658695873019
%C .21.10034.986243.84410206.7314644478.642539662326.56476495490791
%H R. H. Hardin, <a href="/A300427/b300427.txt">Table of n, a(n) for n = 1..241</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2)
%F k=2: a(n) = 3*a(n-1) +a(n-2) -3*a(n-4) -2*a(n-5) -a(n-6) for n>7
%F k=3: [order 13] for n>14
%F k=4: [order 47] for n>49
%e Some solutions for n=5 k=4
%e ..0..0..1..0. .0..0..0..0. .0..1..0..0. .0..0..0..0. .0..1..0..0
%e ..0..1..1..0. .0..1..0..0. .0..1..1..1. .1..0..1..1. .0..1..1..1
%e ..0..0..1..1. .1..1..1..0. .0..0..0..1. .1..0..0..1. .1..0..0..0
%e ..0..1..0..0. .0..0..1..1. .1..1..0..1. .1..1..0..0. .1..0..1..0
%e ..0..1..1..0. .0..0..0..1. .1..0..1..1. .1..1..1..0. .1..1..1..1
%Y Column 1 is A000045(n-1).
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Mar 05 2018
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