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A298240 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. 8

%I

%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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Last modified May 28 15:33 EDT 2020. Contains 334684 sequences. (Running on oeis4.)