A298653 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 6 or 7 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, 5124, 4648, 3820, 6538, 21, 34, 22165, 11529, 14888, 18271, 18271, 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...5124...18271....62544....215035.....739962....2537660

..5...573..1274...4648..18271...75562...291784...1142188....4518674...17656883

..8..1933..3820..14888..62544..291784..1277500...5758443...26328879..118276552

.13..6538.11529..47399.215035.1142188..5758443..30337435..163931288..865848465

.21.22165.34783.150849.739962.4518674.26328879.163931288.1060912744.6689007779

Links

R. H. Hardin, Table of n, a(n) for n = 1..287

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

Example

Some solutions for n=5 k=4
..0..0..0..1. .0..0..1..0. .0..1..0..0. .0..1..1..0. .0..0..1..0
..1..1..1..0. .0..1..0..1. .1..0..1..0. .1..0..0..0. .1..0..1..0
..1..0..0..1. .1..1..0..1. .1..0..1..1. .0..1..1..1. .1..1..1..0
..0..1..1..1. .0..1..0..1. .1..0..0..0. .0..0..0..1. .1..0..1..0
..0..0..0..0. .0..0..1..1. .0..1..1..1. .1..1..1..0. .1..0..1..0

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A297817.

Column 3 is A297988.

Column 4 is A297989.

Sequence in context: A297823 A297993 A298846 * A299607 A297923 A298547

Adjacent sequences: A298650 A298651 A298652 * A298654 A298655 A298656

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 24 2018

Status

approved