A298501 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4 or 7 king-move adjacent elements, with upper left element zero.

1, 2, 2, 3, 4, 3, 5, 3, 3, 5, 8, 13, 1, 13, 8, 13, 34, 4, 4, 34, 13, 21, 73, 5, 38, 5, 73, 21, 34, 203, 6, 54, 54, 6, 203, 34, 55, 594, 20, 97, 281, 97, 20, 594, 55, 89, 1443, 35, 467, 403, 403, 467, 35, 1443, 89, 144, 4013, 70, 1105, 2353, 277, 2353, 1105, 70, 4013, 144, 233

Offset

1,2

Comments

Table starts

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

..2....4..3...13....34....73....203.....594.....1443......4013......11114

..3....3..1....4.....5.....6.....20......35.......70.......174........365

..5...13..4...38....54....97....467....1105.....3354.....12283......37107

..8...34..5...54...281...403...2353...12942....43319....219059....1139692

.13...73..6...97...403...277...1602....6037....19001.....93205.....385257

.21..203.20..467..2353..1602..24272..118439...372820...3857775...22638601

.34..594.35.1105.12942..6037.118439.1377101..4336887..60191437..664833900

.55.1443.70.3354.43319.19001.372820.4336887.10659243.151971896.1550220630

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) = a(n-1) +3*a(n-2) +8*a(n-3) -4*a(n-4) -16*a(n-5) for n>6

k=3: [order 15] for n>16

k=4: [order 51] for n>54

Example

Some solutions for n=6 k=4
..0..1..0..1. .0..0..0..0. .0..1..1..1. .0..0..1..1. .0..0..0..1
..1..0..0..0. .0..0..1..1. .1..1..0..0. .0..0..1..1. .1..1..0..0
..1..1..0..1. .1..1..1..1. .0..1..0..0. .1..0..1..0. .1..1..1..0
..1..1..0..1. .0..0..0..0. .0..1..0..1. .1..0..1..1. .0..0..0..1
..0..0..0..0. .0..0..1..1. .1..1..0..0. .0..0..1..0. .0..0..1..1
..1..1..0..1. .1..1..1..1. .1..1..0..0. .1..0..0..1. .1..1..1..0

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A297901.

Sequence in context: A047675 A187199 A297907 * A298320 A299393 A299194

Adjacent sequences: A298498 A298499 A298500 * A298502 A298503 A298504

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 20 2018

Status

approved