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R. H. Hardin, <a href="/A300342/b300342.txt">Table of n, a(n) for n = 1..180</a>

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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 5, 1, 1, 13, 13, 1, 1, 42, 47, 42, 1, 1, 127, 255, 255, 127, 1, 1, 389, 1272, 2648, 1272, 389, 1, 1, 1192, 6780, 25327, 25327, 6780, 1192, 1, 1, 3645, 36498, 258608, 476507, 258608, 36498, 3645, 1, 1, 11161, 198531, 2697270, 9482056, 9482056

1,5

Table starts

.1.....1.......1.........1...........1..............1................1

.1.....5......13........42.........127............389.............1192

.1....13......47.......255........1272...........6780............36498

.1....42.....255......2648.......25327.........258608..........2697270

.1...127....1272.....25327......476507........9482056........193080853

.1...389....6780....258608.....9482056......366298010......14485201471

.1..1192...36498...2697270...193080853....14485201471....1111703589144

.1..3645..198531..28350215..3949300187...574690828973...85529683934894

.1.11161.1088200.300252749.81288738492.22936158924074.6617480992614301

Empirical for column k:

k=1: a(n) = a(n-1)

k=2: a(n) = a(n-1) +5*a(n-2) +4*a(n-3)

k=3: [order 11] for n>13

k=4: [order 25] for n>26

k=5: [order 66] for n>69

Some solutions for n=5 k=4

..0..0..0..0. .0..1..0..1. .0..0..1..1. .0..1..0..0. .0..0..1..0

..0..0..1..0. .0..0..0..0. .1..0..1..0. .0..0..0..0. .0..0..1..1

..0..1..1..0. .0..1..1..0. .0..0..0..0. .0..0..0..0. .0..1..1..1

..1..1..0..0. .1..1..0..0. .0..0..0..1. .0..0..0..0. .0..0..0..1

..0..1..0..0. .1..0..0..1. .1..0..0..0. .0..0..1..0. .0..0..0..0

Column 2 is A298234.

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R. H. Hardin, Mar 03 2018

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