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%I #4 Mar 16 2018 09:07:02
%S 1,2,2,3,3,3,5,2,2,5,8,3,5,3,8,13,6,12,12,6,13,21,6,19,38,19,6,21,34,
%T 11,47,75,75,47,11,34,55,26,101,186,248,186,101,26,55,89,43,206,530,
%U 836,836,530,206,43,89,144,82,411,1401,2975,3873,2975,1401,411,82,144,233,178
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
%C Table starts
%C ..1..2...3....5.....8.....13......21.......34........55.........89.........144
%C ..2..3...2....3.....6......6......11.......26........43.........82.........178
%C ..3..2...5...12....19.....47.....101......206.......411........882........1851
%C ..5..3..12...38....75....186.....530.....1401......3811......10666.......29764
%C ..8..6..19...75...248....836....2975....10597.....37967.....140091......517221
%C .13..6..47..186...836...3873...16587....77438....373184....1821648.....8941824
%C .21.11.101..530..2975..16587...99717...628078...4085574...26803581...176672818
%C .34.26.206.1401.10597..77438..628078..5562548..48137895..421863566..3738856549
%C .55.43.411.3811.37967.373184.4085574.48137895.556497081.6615843615.79797690689
%H R. H. Hardin, <a href="/A300944/b300944.txt">Table of n, a(n) for n = 1..220</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2)
%F k=2: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) -4*a(n-4) +a(n-5) -2*a(n-6) +a(n-7)
%F k=3: [order 31] for n>32
%e Some solutions for n=5 k=4
%e ..0..1..1..1. .0..1..1..0. .0..0..0..1. .0..1..1..0. .0..1..0..0
%e ..1..1..1..1. .0..0..0..1. .1..0..0..1. .0..0..0..1. .0..0..0..0
%e ..1..1..1..0. .0..0..0..1. .1..1..0..0. .0..0..1..0. .0..1..1..0
%e ..0..0..0..1. .0..0..0..0. .1..1..0..0. .0..1..1..0. .0..0..0..0
%e ..1..0..0..0. .0..0..1..1. .1..1..1..0. .0..1..1..1. .0..0..1..0
%Y Column 1 is A000045(n+1).
%Y Column 2 is A300500.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Mar 16 2018
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