A316289 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 6 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 21, 21, 8, 16, 49, 42, 49, 16, 32, 120, 125, 125, 120, 32, 64, 293, 361, 354, 361, 293, 64, 128, 719, 987, 1372, 1372, 987, 719, 128, 256, 1774, 2840, 3933, 7973, 3933, 2840, 1774, 256, 512, 4389, 8177, 12454, 35706, 35706, 12454, 8177, 4389

Offset

1,2

Comments

Table starts

...1....2.....4......8......16.......32........64.........128..........256

...2....8....21.....49.....120......293.......719........1774.........4389

...4...21....42....125.....361......987......2840........8177........23078

...8...49...125....354....1372.....3933.....12454.......42946.......135396

..16..120...361...1372....7973....35706....164734......838632......4054621

..32..293...987...3933...35706...205946...1262767.....8828402.....57330292

..64..719..2840..12454..164734..1262767..10464990...101136854....901515338

.128.1774..8177..42946..838632..8828402.101136854..1363011634..17053088411

.256.4389.23078.135396.4054621.57330292.901515338.17053088411.297013482603

Links

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

Formula

Empirical for column k:

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

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

k=3: [order 10] for n>12

k=4: [order 21] for n>25

k=5: [order 85] for n>89

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A303721.

Sequence in context: A304775 A316518 A304472 * A306053 A317230 A304310

Adjacent sequences: A316286 A316287 A316288 * A316290 A316291 A316292

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 28 2018

Status

approved