A296588 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 0, 2 or 3 neighboring 1s.

2, 3, 3, 5, 9, 5, 8, 22, 22, 8, 13, 62, 83, 62, 13, 21, 172, 346, 346, 172, 21, 34, 480, 1465, 2458, 1465, 480, 34, 55, 1358, 6241, 17503, 17503, 6241, 1358, 55, 89, 3849, 26895, 125765, 214830, 125765, 26895, 3849, 89, 144, 10951, 116541, 923475, 2607478

Offset

1,1

Comments

Table starts

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

..3.....9.....22.......62........172..........480...........1358

..5....22.....83......346.......1465.........6241..........26895

..8....62....346.....2458......17503.......125765.........923475

.13...172...1465....17503.....214830......2607478.......32689069

.21...480...6241...125765....2607478.....52756072.....1109882746

.34..1358..26895...923475...32689069...1109882746....39585589653

.55..3849.116541..6803610..410639937..23359296497..1408384872667

.89.10951.507102.50377421.5176790260.492457987101.50119033383361

Links

R. H. Hardin, Table of n, a(n) for n = 1..264

Formula

Empirical for column k:

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

k=2: a(n) = 3*a(n-1) +a(n-2) -a(n-3) -8*a(n-4) -3*a(n-6) -2*a(n-7) -5*a(n-8) +a(n-9)

k=3: [order 21]

k=4: [order 57]

Example

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

Crossrefs

Column 1 is A000045(n+2).

Sequence in context: A194000 A295781 A296725 * A065460 A241741 A175147

Adjacent sequences: A296585 A296586 A296587 * A296589 A296590 A296591

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 16 2017

Status

approved