A295918 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 0 or 3 king-move neighboring 1s.

2, 3, 3, 5, 6, 5, 8, 13, 13, 8, 13, 28, 39, 28, 13, 21, 60, 115, 115, 60, 21, 34, 129, 337, 467, 337, 129, 34, 55, 277, 993, 1880, 1880, 993, 277, 55, 89, 595, 2919, 7604, 10290, 7604, 2919, 595, 89, 144, 1278, 8587, 30721, 56955, 56955, 30721, 8587, 1278, 144, 233

Offset: 1

Author

R. H. Hardin, Nov 29 2017

Keywords

• nonn
• tabl

Comments

Table starts

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

..3....6....13.....28......60.......129........277.........595..........1278

..5...13....39....115.....337.......993.......2919........8587.........25257

..8...28...115....467....1880......7604......30721......124117........501512

.13...60...337...1880...10290.....56955.....314044.....1732883.......9562608

.21..129...993...7604...56955....431844....3261576....24650278.....186318117

.34..277..2919..30721..314044...3261576...33703065...348555744....3605337986

.55..595..8587.124117.1732883..24650278..348555744..4933593439...69844332764

.89.1278.25257.501512.9562608.186318117.3605337986.69844332764.1353357158724

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..311

Crossrefs

Column 1 is A000045(n+2).

Column 2 is A002478(n+1).

Formula

Empirical for column k:

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

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

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

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

k=5: [order 38]

k=6: [order 92]