A298167 T(n,k)=Number of nXk 0..1 arrays with every element equal to 3, 4, 5 or 8 king-move adjacent elements, with upper left element zero.

0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 1, 2, 0, 0, 3, 2, 2, 3, 0, 0, 5, 3, 4, 3, 5, 0, 0, 8, 5, 6, 6, 5, 8, 0, 0, 13, 8, 11, 10, 11, 8, 13, 0, 0, 21, 13, 18, 18, 18, 18, 13, 21, 0, 0, 34, 21, 31, 32, 62, 32, 31, 21, 34, 0, 0, 55, 34, 53, 80, 133, 133, 80, 53, 34, 55, 0, 0, 89, 55, 91, 171, 749, 624

Offset

1,12

Comments

Table starts

.0..0..0..0...0....0.....0......0.......0.........0..........0...........0

.0..1..1..2...3....5.....8.....13......21........34.........55..........89

.0..1..1..2...3....5.....8.....13......21........34.........55..........89

.0..2..2..4...6...11....18.....31......53........91........156.........269

.0..3..3..6..10...18....32.....80.....171.......528.......1439........4889

.0..5..5.11..18...62...133....749....2248.....11243......43303......213698

.0..8..8.18..32..133...624...4525...22143....189512....1055639.....8706804

.0.13.13.31..80..749..4525..95458..763536..11467153..117226402..1544912726

.0.21.21.53.171.2248.22143.763536.6564438.187830170.2268628157.49711027609

Links

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

Formula

Empirical for column k:

k=1: a(n) =

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

k=3: a(n) = a(n-1) +a(n-2)

k=4: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) -2*a(n-5) +a(n-6) +a(n-7)

k=5: [order 67]

Example

Some solutions for n=8 k=4
..0..0..1..1. .0..0..0..0. .0..0..1..1. .0..0..1..1. .0..0..1..1
..0..0..1..1. .0..0..0..0. .0..0..1..1. .0..0..1..1. .0..0..1..1
..1..1..0..0. .1..1..1..1. .0..0..1..1. .1..1..0..0. .0..1..0..1
..1..1..0..0. .1..1..1..1. .0..1..0..1. .1..1..0..0. .1..0..1..0
..1..1..0..0. .1..1..1..1. .1..0..1..0. .0..0..1..1. .1..1..0..0
..0..0..1..1. .0..0..0..0. .1..1..0..0. .0..0..1..1. .1..1..0..0
..0..0..1..1. .0..0..0..0. .1..1..0..0. .1..1..0..0. .0..0..1..1
..0..0..1..1. .0..0..0..0. .1..1..0..0. .1..1..0..0. .0..0..1..1

Crossrefs

Column 2 is A000045(n-1).

Column 3 is A000045(n-1).

Sequence in context: A298187 A298183 A098356 * A298957 A298902 A298963

Adjacent sequences: A298164 A298165 A298166 * A298168 A298169 A298170

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 14 2018

Status

approved