A299451 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 3, 4, 3, 5, 4, 4, 5, 8, 8, 1, 8, 8, 13, 32, 4, 4, 32, 13, 21, 32, 10, 21, 10, 32, 21, 34, 64, 6, 32, 32, 6, 64, 34, 55, 256, 11, 36, 231, 36, 11, 256, 55, 89, 256, 41, 161, 163, 163, 161, 41, 256, 89, 144, 512, 24, 264, 546, 211, 546, 264, 24, 512, 144, 233, 2048, 42, 430

Offset

1,2

Comments

Table starts

..1...2..3...5....8...13....21.....34.....55......89......144.......233

..2...4..4...8...32...32....64....256....256.....512.....2048......2048

..3...4..1...4...10....6....11.....41.....24......42......169.......100

..5...8..4..21...32...36...161....264....430....1475.....2598......4872

..8..32.10..32..231..163...546...2904...2321....8729....37095.....34873

.13..32..6..36..163..211...804...3138...4869...21921....69029....124071

.21..64.11.161..546..804..6326..19745..39495..290364...855008...2191987

.34.256.41.264.2904.3138.19745.174794.205522.1778833.11489465..16992517

.55.256.24.430.2321.4869.39495.205522.665961.5936888.26103440.114805573

Links

R. H. Hardin, Table of n, a(n) for n = 1..241

Formula

Empirical for column k:

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

k=2: a(n) = 8*a(n-3) for n>4

k=3: [order 18] for n>19

k=4: [order 62] for n>63

Example

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

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A096252(n-1).

Sequence in context: A299194 A300030 A232451 * A300089 A298230 A298154

Adjacent sequences: A299448 A299449 A299450 * A299452 A299453 A299454

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 10 2018

Status

approved