A300472 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 29, 29, 8, 16, 108, 160, 108, 16, 32, 401, 925, 925, 401, 32, 64, 1490, 5363, 8608, 5363, 1490, 64, 128, 5536, 31106, 80914, 80914, 31106, 5536, 128, 256, 20569, 180397, 759100, 1231578, 759100, 180397, 20569, 256, 512, 76424, 1046223

Offset: 1

Author

R. H. Hardin, Mar 06 2018

Keywords

• nonn
• tabl

Comments

Table starts

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

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

...4....29.....160.......925........5363.........31106..........180397

...8...108.....925......8608.......80914........759100.........7121067

..16...401....5363.....80914.....1231578......18735889.......284885784

..32..1490...31106....759100....18735889.....462538206.....11408562672

..64..5536..180397...7121067...284885784...11408562672....456303004550

.128.20569.1046223..66808673..4332278363..281433652906..18253046515989

.256.76424.6067629.626787854.65881928079.6942908646999.730219136878799

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..264

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

k=4: [order 22]

k=5: [order 58] for n>59