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

1,1

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

Links

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

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]

Example

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

Crossrefs

Column 1 is A000045(n+2).

Column 2 is A002478(n+1).

Sequence in context: A064464 A094585 A183322 * A296834 A242642 A178041

Adjacent sequences: A295915 A295916 A295917 * A295919 A295920 A295921

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 29 2017

Status

approved