login
A296834
T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 0, 3 or 5 king-move neighboring 1s.
7
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 21 2017
STATUS
approved