A299081 T(n,k) = Number of n X k 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 7 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 31, 31, 8, 16, 121, 163, 121, 16, 32, 472, 927, 927, 472, 32, 64, 1841, 5331, 8245, 5331, 1841, 64, 128, 7181, 30535, 74329, 74329, 30535, 7181, 128, 256, 28010, 175286, 664377, 1055999, 664377, 175286, 28010, 256, 512, 109255, 1006611

Offset

1,2

Comments

Table starts

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

...2......8......31.......121.........472..........1841............7181

...4.....31.....163.......927........5331.........30535..........175286

...8....121.....927......8245.......74329........664377.........5966905

..16....472....5331.....74329.....1055999......14831527.......209649724

..32...1841...30535....664377....14831527.....325878090......7216923643

..64...7181..175286...5966905...209649724....7216923643....250915355467

.128..28010.1006611..53667656..2971224409..160460154889...8769918141746

.256.109255.5780036.482603686.42096980790.3565905309360.306309018507458

Links

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

Formula

Empirical for column k:

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

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

k=3: [order 10] for n>11

k=4: [order 30] for n>31

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A281831.

Sequence in context: A316822 A317572 A281837 * A299844 A299001 A299746

Adjacent sequences: A299078 A299079 A299080 * A299082 A299083 A299084

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 02 2018

Status

approved