A299001 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 6 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 31, 31, 8, 16, 121, 179, 121, 16, 32, 472, 1073, 1073, 472, 32, 64, 1841, 6479, 10150, 6479, 1841, 64, 128, 7181, 39015, 97462, 97462, 39015, 7181, 128, 256, 28010, 235033, 932318, 1502511, 932318, 235033, 28010, 256, 512, 109255, 1416220

Offset

1,2

Comments

Table starts

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

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

...4.....31.....179......1073........6479.........39015..........235033

...8....121....1073.....10150.......97462........932318.........8918662

..16....472....6479.....97462.....1502511......23031390.......353088569

..32...1841...39015....932318....23031390.....564821426.....13849577141

..64...7181..235033...8918662...353088569...13849577141....543022804167

.128..28010.1416220..85379274..5420414253..340272636359..21348528789475

.256.109255.8533123.817325435.83214520668.8360888694306.839394891016021

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 37] for n>38

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A281831.

Sequence in context: A281837 A299081 A299844 * A299746 A299668 A300259

Adjacent sequences: A298998 A298999 A299000 * A299002 A299003 A299004

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 31 2018

Status

approved