A299844 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 7 or 8 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, 1056001, 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.....1056001......14831535.......209649848

..32...1841...30535....664377....14831535.....325878154......7216925214

..64...7181..175286...5966905...209649848....7216925214....250915415042

.128..28010.1006611..53667656..2971226455..160460196001...8769920586285

.256.109255.5780036.482603686.42097006186.3565906147902.306309096924610

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..1..0. .0..1..1..0. .0..0..1..1. .0..0..0..1. .0..0..0..0
..0..0..0..1. .1..0..1..1. .1..0..0..1. .1..1..1..1. .1..1..1..0
..1..1..0..1. .1..0..0..0. .1..1..0..1. .0..0..0..0. .0..0..0..1
..1..0..0..1. .0..1..1..1. .0..1..0..1. .0..1..1..1. .0..1..0..0
..1..0..1..1. .1..0..1..1. .0..0..1..0. .0..0..0..1. .0..1..0..1

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A281831.

Column 3 is A299076.

Column 4 is A299077.

Sequence in context: A317572 A281837 A299081 * A299001 A299746 A299668

Adjacent sequences: A299841 A299842 A299843 * A299845 A299846 A299847

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 20 2018

Status

approved