A296834 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 0, 3 or 5 king-move neighboring 1s.

2, 3, 3, 5, 6, 5, 8, 14, 14, 8, 13, 31, 43, 31, 13, 21, 70, 132, 132, 70, 21, 34, 157, 402, 573, 402, 157, 34, 55, 353, 1230, 2441, 2441, 1230, 353, 55, 89, 793, 3755, 10485, 14379, 10485, 3755, 793, 89, 144, 1782, 11475, 44951, 85500, 85500, 44951, 11475, 1782, 144

Offset: 1

Author

R. H. Hardin, Dec 21 2017

Keywords

• nonn
• tabl

Comments

Table starts

..2....3.....5......8.......13........21.........34...........55............89

..3....6....14.....31.......70.......157........353..........793..........1782

..5...14....43....132......402......1230.......3755........11475.........35054

..8...31...132....573.....2441.....10485......44951.......192730........826498

.13...70...402...2441....14379.....85500.....508111......3017667......17931240

.21..157..1230..10485....85500....706534....5834429.....48122349.....397252886

.34..353..3755..44951...508111...5834429...67007971....768117235....8815633972

.55..793.11475.192730..3017667..48122349..768117235..12228697715..194991656916

.89.1782.35054.826498.17931240.397252886.8815633972.194991656916.4321362259224

Examples

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

Links

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

Crossrefs

Column 1 is A000045(n+2).

Column 2 is A006356.

Formula

Empirical for column k:

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

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

k=3: [order 15]

k=4: [order 50]