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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. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified February 1 03:45 EST 2023. Contains 359981 sequences. (Running on oeis4.)