A299654 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 247, 128, 16, 32, 512, 1924, 1924, 512, 32, 64, 2048, 14981, 29408, 14981, 2048, 64, 128, 8192, 116654, 448993, 448993, 116654, 8192, 128, 256, 32768, 908360, 6856789, 13431706, 6856789, 908360, 32768, 256, 512, 131072

Offset

1,2

Comments

Table starts

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

...2......8.......32.........128............512.............2048

...4.....32......247........1924..........14981...........116654

...8....128.....1924.......29408.........448993..........6856789

..16....512....14981......448993.......13431706........401989538

..32...2048...116654.....6856789......401989538......23582064542

..64...8192...908360...104711327....12030404350....1383316377321

.128..32768..7073213..1599074414...360039414559...81146123707386

.256.131072.55077652.24419877459.10775053220325.4760069868306954

Links

R. H. Hardin, Table of n, a(n) for n = 1..241

Formula

Empirical for column k:

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

k=2: a(n) = 4*a(n-1)

k=3: a(n) = 7*a(n-1) +5*a(n-2) +9*a(n-3) -a(n-4) -6*a(n-5)

k=4: [order 14]

k=5: [order 31]

k=6: [order 89]

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A004171(n-1).

Sequence in context: A302010 A301784 A316808 * A317525 A300208 A303421

Adjacent sequences: A299651 A299652 A299653 * A299655 A299656 A299657

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 15 2018

Status

approved