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R. H. Hardin, <a href="/A297993/b297993.txt">Table of n, a(n) for n = 1..364</a>

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

0, 1, 1, 1, 4, 1, 2, 17, 17, 2, 3, 49, 48, 49, 3, 5, 166, 146, 146, 166, 5, 8, 573, 424, 466, 424, 573, 8, 13, 1933, 1274, 1446, 1446, 1274, 1933, 13, 21, 6538, 3820, 4648, 5100, 4648, 3820, 6538, 21, 34, 22165, 11529, 14888, 18189, 18189, 14888, 11529, 22165, 34

1,5

Table starts

..0.....1.....1......2......3.......5........8........13.........21.........34

..1.....4....17.....49....166.....573.....1933......6538......22165......75089

..1....17....48....146....424....1274.....3820.....11529......34783.....104826

..2....49...146....466...1446....4648....14888.....47399.....150849.....480015

..3...166...424...1446...5100...18189....62390....213997.....735000....2520806

..5...573..1274...4648..18189...74675...290466...1134198....4475863...17501388

..8..1933..3820..14888..62390..290466..1276012...5745438...26249179..117931466

.13..6538.11529..47399.213997.1134198..5745438..30240388..163303980..862771193

.21.22165.34783.150849.735000.4475863.26249179.163303980.1056360518.6667346762

Empirical for column k:

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

k=2: a(n) = 3*a(n-1) +a(n-2) +2*a(n-3) -2*a(n-4) -4*a(n-5) for n>6

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

k=4: [order 24] for n>27

k=5: [order 99] for n>104

Some solutions for n=6 k=4

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

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

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

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

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

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

Column 1 is A000045(n-1).

Column 2 is A297817.

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nonn,tabl

R. H. Hardin, Jan 10 2018

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