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%I #8 Jan 29 2018 05:10:44
%S 1,1,1,1,5,1,1,13,13,1,1,42,22,42,1,1,127,124,124,127,1,1,389,409,
%T 1156,409,389,1,1,1192,1921,8117,8117,1921,1192,1,1,3645,8908,66626,
%U 107163,66626,8908,3645,1,1,11161,41933,563826,1636306,1636306,563826,41933
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4 or 5 king-move adjacent elements, with upper left element zero.
%C Table starts
%C .1.....1......1........1..........1.............1...............1
%C .1.....5.....13.......42........127...........389............1192
%C .1....13.....22......124........409..........1921............8908
%C .1....42....124.....1156.......8117.........66626..........563826
%C .1...127....409.....8117.....107163.......1636306........25784604
%C .1...389...1921....66626....1636306......45356726......1300110664
%C .1..1192...8908...563826...25784604....1300110664.....67668568376
%C .1..3645..41933..4788445..403231105...36992129471...3503621681315
%C .1.11161.204016.41239301.6388232748.1065292018400.183337397269876
%H R. H. Hardin, <a href="/A298240/b298240.txt">Table of n, a(n) for n = 1..180</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = a(n-1) +5*a(n-2) +4*a(n-3) with g.f. (1-x^2-x^3)/(1-x-5*x^2-4*x^3).
%F k=3: [order 13] for n>15
%F k=4: [order 47] for n>49
%e Some solutions for n=5 k=4
%e ..0..0..0..1. .0..1..1..0. .0..1..1..0. .0..1..1..1. .0..0..1..1
%e ..0..1..0..0. .1..1..0..0. .1..1..0..0. .1..1..0..1. .1..0..1..0
%e ..1..1..0..1. .0..0..1..0. .1..0..1..1. .0..1..0..0. .1..1..0..0
%e ..1..0..0..0. .0..0..1..1. .0..0..1..0. .1..1..0..0. .1..1..0..0
%e ..0..0..0..1. .0..0..1..0. .0..0..0..0. .1..1..0..1. .1..1..0..0
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jan 15 2018
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