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%I #4 Aug 15 2018 13:28:17
%S 1,2,2,3,3,3,5,4,4,5,8,7,5,7,8,13,11,11,11,11,13,21,18,18,22,18,18,21,
%T 34,30,32,34,34,32,30,34,55,49,54,64,51,64,54,49,55,89,81,98,132,126,
%U 126,132,98,81,89,144,134,173,280,272,314,272,280,173,134,144,233,221,315
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3 or 5 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.....233......377
%C ..2..3...4...7...11...18....30....49.....81....134.....221.....365......603
%C ..3..4...5..11...18...32....54....98....173....315.....559....1008.....1813
%C ..5..7..11..22...34...64...132...280....556...1083....2208....4480.....9083
%C ..8.11..18..34...51..126...272...616...1347...2910....6602...15218....34152
%C .13.18..32..64..126..314...699..1778...4262..10254...25322...63395...158636
%C .21.30..54.132..272..699..1851..5189..13410..35181...97580..275205...756872
%C .34.49..98.280..616.1778..5189.15876..44305.131008..401009.1258378..3868741
%C .55.81.173.556.1347.4262.13410.44305.139346.466676.1583947.5508419.18965058
%H R. H. Hardin, <a href="/A318082/b318082.txt">Table of n, a(n) for n = 1..312</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2)
%F k=2: a(n) = a(n-1) +2*a(n-3) -a(n-6)
%F k=3: [order 24]
%e Some solutions for n=5 k=4
%e ..0..0..1..1. .0..0..1..0. .0..0..0..0. .0..1..0..0. .0..0..0..1
%e ..0..0..0..1. .0..0..1..1. .0..0..0..0. .0..1..1..0. .0..0..0..0
%e ..1..1..1..1. .0..1..0..0. .0..0..0..1. .1..0..0..0. .0..0..0..0
%e ..0..1..1..1. .0..0..0..0. .0..1..1..0. .0..0..0..0. .0..0..0..0
%e ..0..0..1..1. .0..0..0..0. .0..0..1..0. .0..0..0..0. .1..0..0..0
%Y Column 1 is A000045(n+1).
%Y Column 2 is A317767.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Aug 15 2018
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