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%I #4 Feb 11 2018 06:16:11
%S 1,1,1,1,1,1,1,1,1,1,1,2,12,2,1,1,5,5,5,5,1,1,9,33,8,33,9,1,1,22,55,
%T 41,41,55,22,1,1,45,132,117,285,117,132,45,1,1,101,272,476,1540,1540,
%U 476,272,101,1,1,218,630,1743,5869,12411,5869,1743,630,218,1,1,477,1355,7078
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C .1...1...1....1......1.......1.........1..........1............1.............1
%C .1...1...1....2......5.......9........22.........45..........101...........218
%C .1...1..12....5.....33......55.......132........272..........630..........1355
%C .1...2...5....8.....41.....117.......476.......1743.........7078.........28743
%C .1...5..33...41....285....1540......5869......31464.......164344........875093
%C .1...9..55..117...1540...12411.....89125.....826509......7492106......69199615
%C .1..22.132..476...5869...89125....902141...12982595....174024827....2513147146
%C .1..45.272.1743..31464..826509..12982595..310347496...6868847887..161346598727
%C .1.101.630.7078.164344.7492106.174024827.6868847887.249358437986.9535286392860
%H R. H. Hardin, <a href="/A299521/b299521.txt">Table of n, a(n) for n = 1..197</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = a(n-1) +3*a(n-2) -2*a(n-4) for n>5
%F k=3: [order 12] for n>13
%F k=4: [order 34] for n>36
%e Some solutions for n=5 k=4
%e ..0..0..1..1. .0..0..1..1. .0..1..1..1. .0..0..1..1. .0..0..1..1
%e ..0..0..1..1. .0..0..1..1. .1..1..1..1. .0..0..1..1. .0..0..1..1
%e ..1..1..1..0. .0..0..0..0. .0..1..1..1. .0..0..1..1. .0..0..1..1
%e ..1..1..1..1. .1..1..0..0. .1..1..0..0. .0..0..1..1. .1..1..1..1
%e ..1..1..1..0. .1..1..0..0. .1..1..0..0. .0..0..1..1. .1..1..1..0
%Y Column 2 is A052962(n-2).
%K nonn,tabl
%O 1,12
%A _R. H. Hardin_, Feb 11 2018
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