A316376 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 4, 6 or 8 king-move adjacent elements, with upper left element zero.

1, 1, 1, 1, 4, 1, 1, 8, 8, 1, 1, 24, 13, 24, 1, 1, 82, 60, 60, 82, 1, 1, 272, 217, 418, 217, 272, 1, 1, 908, 749, 2186, 2186, 749, 908, 1, 1, 3076, 2822, 12281, 16817, 12281, 2822, 3076, 1, 1, 10444, 10516, 72713, 128585, 128585, 72713, 10516, 10444, 1, 1, 35480, 38934

Offset

1,5

Comments

Table starts

.1.....1.....1.......1........1..........1...........1.............1

.1.....4.....8......24.......82........272.........908..........3076

.1.....8....13......60......217........749........2822.........10516

.1....24....60.....418.....2186......12281.......72713........423041

.1....82...217....2186....16817.....128585.....1076888.......8858964

.1...272...749...12281...128585....1396959....16730969.....194865364

.1...908..2822...72713..1076888...16730969...294007902....4935143895

.1..3076.10516..423041..8858964..194865364..4935143895..118878261056

.1.10444.38934.2465234.72193958.2259023326.82582592407.2848273549547

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

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

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

k=3: [order 20] for n>21

k=4: [order 70] for n>72

Example

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

Crossrefs

Column 2 is A303882.

Column 3 is A304546.

Column 4 is A304547.

Sequence in context: A304894 A316576 A304551 * A306136 A317271 A304419

Adjacent sequences: A316373 A316374 A316375 * A316377 A316378 A316379

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 30 2018

Status

approved