A300811 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 29, 29, 8, 16, 108, 170, 108, 16, 32, 401, 1004, 1004, 401, 32, 64, 1490, 5908, 9504, 5908, 1490, 64, 128, 5536, 34836, 90980, 90980, 34836, 5536, 128, 256, 20569, 205369, 872495, 1415898, 872495, 205369, 20569, 256, 512, 76424, 1210811

Offset

1,2

Comments

Table starts

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

...2.....8......29.......108.........401..........1490............5536

...4....29.....170......1004........5908.........34836..........205369

...8...108....1004......9504.......90980........872495.........8363710

..16...401....5908.....90980.....1415898......22066384.......343667594

..32..1490...34836....872495....22066384.....559634028.....14189038853

..64..5536..205369...8363710...343667594...14189038853....585611214958

.128.20569.1210811..80174942..5352803078..359766695966..24166702223161

.256.76424.7138574.768542846.83370618870.9121562946307.997271941003944

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

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) -a(n-3) -a(n-4)

k=3: [order 13]

k=4: [order 40]

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A220547.

Sequence in context: A208709 A300472 A326105 * A301450 A302265 A302965

Adjacent sequences: A300808 A300809 A300810 * A300812 A300813 A300814

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 13 2018

Status

approved