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R. H. Hardin, <a href="/A316552/b316552.txt">Table of n, a(n) for n = 1..263</a>

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

1, 2, 2, 3, 5, 3, 5, 7, 7, 5, 8, 17, 10, 17, 8, 13, 35, 17, 17, 35, 13, 21, 61, 36, 42, 36, 61, 21, 34, 127, 69, 89, 89, 69, 127, 34, 55, 265, 129, 187, 251, 187, 129, 265, 55, 89, 507, 260, 430, 621, 621, 430, 260, 507, 89, 144, 1013, 544, 1046, 1568, 1811, 1568, 1046, 544

1,2

Table starts

..1...2...3....5.....8....13.....21......34......55.......89.......144

..2...5...7...17....35....61....127.....265.....507.....1013......2071

..3...7..10...17....36....69....129.....260.....544.....1125......2348

..5..17..17...42....89...187....430....1046....2407.....5706.....13873

..8..35..36...89...251...621...1568....4269...11869....33451.....95326

.13..61..69..187...621..1811...5265...17004...54443...174625....570128

.21.127.129..430..1568..5265..18978...73409..276005..1055277...4099795

.34.265.260.1046..4269.17004..73409..336604.1492856..6793881..31252764

.55.507.544.2407.11869.54443.276005.1492856.7870292.42144065.228096346

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2)

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

k=3: [order 15]

k=4: [order 45] for n>48

Some solutions for n=5 k=4

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

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

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

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

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

Column 1 is A000045(n+1).

Column 2 is A303802.

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nonn,tabl

R. H. Hardin, Jul 06 2018

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