A299607 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 6, 7 or 8 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, 5125, 4648, 3820, 6538, 21, 34, 22165, 11529, 14888, 18273, 18273, 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...5125...18273....62547....215175.....740442....2539018

..5...573..1274...4648..18273...75970...292458...1146690....4552661...17798866

..8..1933..3820..14888..62547..292458..1284100...5779019...26461571..119048834

.13..6538.11529..47399.215175.1146690..5779019..30465069..164752420..870288036

.21.22165.34783.150849.740442.4552661.26461571.164752420.1069988410.6740006098

Links

R. H. Hardin, Table of n, a(n) for n = 1..264

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=6 k=6
..0..1..0..1..1..0. .0..0..1..1..0..1. .0..1..1..0..0..0. .0..0..1..0..1..0
..1..0..1..1..0..1. .1..1..0..1..1..0. .1..0..1..1..1..0. .1..1..0..0..0..1
..1..1..1..1..1..0. .0..0..1..1..1..1. .1..1..1..1..1..0. .0..0..0..0..0..0
..0..1..1..1..1..1. .1..1..1..1..1..0. .1..0..1..1..1..1. .0..0..0..0..0..1
..0..1..1..1..1..0. .1..1..1..1..1..0. .0..1..0..1..1..0. .1..1..0..0..1..0
..0..0..0..1..0..1. .0..0..1..0..0..0. .1..0..0..1..1..0. .0..0..1..0..0..1

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A297817.

Column 3 is A297988.

Column 4 is A297989.

Sequence in context: A297993 A298846 A298653 * A297923 A298547 A298337

Adjacent sequences: A299604 A299605 A299606 * A299608 A299609 A299610

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 14 2018

Status

approved