A301450 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 5 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 29, 29, 8, 16, 108, 171, 108, 16, 32, 401, 1008, 1008, 401, 32, 64, 1490, 5930, 9541, 5930, 1490, 64, 128, 5536, 34976, 91370, 91370, 34976, 5536, 128, 256, 20569, 206266, 877044, 1423344, 877044, 206266, 20569, 256, 512, 76424, 1216562

Offset: 1

Author

R. H. Hardin, Mar 21 2018

Keywords

• nonn
• tabl

Comments

Table starts

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

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

...4....29.....171......1008........5930.........34976...........206266

...8...108....1008......9541.......91370........877044..........8414314

..16...401....5930.....91370.....1423344......22207589........346263718

..32..1490...34976....877044....22207589.....564002959......14319674594

..64..5536..206266...8414314...346263718...14319674594.....592006690060

.128.20569.1216562..80726964..5399605493..363595763125...24472344492129

.256.76424.7175157.774477323.84198470831.9231743942243.1011614229196954

Examples

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

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]