A300089 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 5, 6, 7 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, 25, 10, 32, 21, 34, 64, 6, 50, 50, 6, 64, 34, 55, 256, 19, 98, 415, 98, 19, 256, 55, 89, 256, 41, 359, 533, 533, 359, 41, 256, 89, 144, 512, 32, 766, 3089, 1822, 3089, 766, 32, 512, 144, 233, 2048, 106

Offset

1,2

Comments

Table starts

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

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

..3...4..1....4....10......6......19........41.........32.........106

..5...8..4...25....50.....98.....359.......766.......1932........5677

..8..32.10...50...415....533....3089.....13808......27523......150838

.13..32..6...98...533...1822...13646.....64560.....292356.....1935206

.21..64.19..359..3089..13646..167131...1179926....7203918....75245386

.34.256.41..766.13808..64560.1179926..14634300..102798960..1708342471

.55.256.32.1932.27523.292356.7203918.102798960.1518807971.32115302281

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

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 20] for n>21

k=4: [order 59] for n>61

Example

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

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A096252(n-1).

Sequence in context: A300030 A232451 A299451 * A298230 A298154 A299128

Adjacent sequences: A300086 A300087 A300088 * A300090 A300091 A300092

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 24 2018

Status

approved