A297993 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

Offset

1,5

Comments

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

Links

R. H. Hardin, Table of n, a(n) for n = 1..364

Formula

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

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A297817.

Sequence in context: A284771 A283042 A297823 * A298846 A298653 A299607

Adjacent sequences: A297990 A297991 A297992 * A297994 A297995 A297996

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 10 2018

Status

approved