A303242 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

1, 1, 2, 1, 2, 4, 1, 11, 2, 8, 1, 13, 18, 3, 16, 1, 34, 8, 55, 6, 32, 1, 65, 60, 10, 181, 10, 64, 1, 123, 56, 255, 61, 494, 21, 128, 1, 266, 236, 149, 1106, 160, 1465, 42, 256, 1, 499, 428, 1676, 1373, 5158, 458, 4415, 86, 512, 1, 1037, 1248, 3307, 11111, 7823, 23995, 1748

Offset: 1

Author

R. H. Hardin, Apr 20 2018

Keywords

• nonn
• tabl

Comments

Table starts

...1..1.....1....1......1.......1........1.........1..........1............1

...2..2....11...13.....34......65......123.......266........499.........1037

...4..2....18....8.....60......56......236.......428.......1248.........3264

...8..3....55...10....255.....149.....1676......3307......18505........65498

..16..6...181...61...1106....1373....11111.....38480.....221943......1162591

..32.10...494..160...5158....7823....90728....421983....3251872.....23282610

..64.21..1465..458..23995...41878...686376...4288552...44547581....435326091

.128.42..4415.1748.108726..277018..5320294..48315454..648070597...8762716079

.256.86.12934.6056.506416.1721671.42575026.536745912.9508520220.176408218876

Examples

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

Links

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A240513(n-2).

Row 2 is A297870(n+2).

Formula

Empirical for column k:

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

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

k=3: [order 13]

k=4: [order 71] for n>72

Empirical for row n:

n=1: a(n) = a(n-1)

n=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5

n=3: [order 20]

n=4: [order 67] for n>68