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

1,1

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

Links

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

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]

Example

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

Crossrefs

Column 1 is A000045(n+2).

Column 2 is A006356.

Sequence in context: A094585 A183322 A295918 * A242642 A178041 A181805

Adjacent sequences: A296831 A296832 A296833 * A296835 A296836 A296837

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 21 2017

Status

approved