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

Author

R. H. Hardin, Mar 13 2018

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A220547.

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]