A298846 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 6 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, 5101, 4648, 3820, 6538, 21, 34, 22165, 11529, 14888, 18191, 18191, 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...5101...18191....62393....214017.....735090....2521128

..5...573..1274...4648..18191...74685...290474...1134326....4476521...17504192

..8..1933..3820..14888..62393..290474..1276034...5745665...26250580..117940632

.13..6538.11529..47399.214017.1134326..5745665..30242236..163316554..862848634

.21.22165.34783.150849.735090.4476521.26250580.163316554.1056423010.6667708149

Links

R. H. Hardin, Table of n, a(n) for n = 1..337

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A297817.

Column 3 is A297988.

Column 4 is A297989.

Sequence in context: A283042 A297823 A297993 * A298653 A299607 A297923

Adjacent sequences: A298843 A298844 A298845 * A298847 A298848 A298849

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 27 2018

Status

approved