A295606 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 2, 3 or 4 1s.

2, 3, 3, 5, 8, 5, 8, 20, 20, 8, 13, 51, 83, 51, 13, 21, 132, 338, 338, 132, 21, 34, 341, 1425, 2305, 1425, 341, 34, 55, 883, 6080, 16340, 16340, 6080, 883, 55, 89, 2293, 26249, 119371, 201602, 119371, 26249, 2293, 89, 144, 5964, 114298, 892086, 2594128

Offset

1,1

Comments

Table starts

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

..3....8.....20.......51........132..........341.............883

..5...20.....83......338.......1425.........6080...........26249

..8...51....338.....2305......16340.......119371..........892086

.13..132...1425....16340.....201602......2594128........34416318

.21..341...6080...119371....2594128.....59562253......1412108105

.34..883..26249...892086...34416318...1412108105.....59768294027

.55.2293.114298..6775059..465449155..34084604345...2568256527624

.89.5964.501405.52046892.6367873016.830405539405.111128604535696

Links

R. H. Hardin, Table of n, a(n) for n = 1..287

Formula

Empirical for column k:

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

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

k=3: [order 12]

k=4: [order 27]

k=5: [order 69]

Example

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

Crossrefs

Column 1 is A000045(n+2).

Column 2 is A295346.

Sequence in context: A295051 A295379 A295352 * A154690 A046937 A247309

Adjacent sequences: A295603 A295604 A295605 * A295607 A295608 A295609

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 24 2017

Status

approved