A295531 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 1, 2 or 4 1s.

1, 2, 2, 4, 10, 4, 7, 29, 29, 7, 12, 87, 147, 87, 12, 21, 280, 774, 774, 280, 21, 37, 876, 4080, 7071, 4080, 876, 37, 65, 2735, 21489, 64189, 64189, 21489, 2735, 65, 114, 8583, 113466, 588529, 1012315, 588529, 113466, 8583, 114, 200, 26900, 598374, 5400933

Offset

1,2

Comments

Table starts

...1.....2.......4.........7..........12............21...............37

...2....10......29........87.........280...........876.............2735

...4....29.....147.......774........4080.........21489...........113466

...7....87.....774......7071.......64189........588529..........5400933

..12...280....4080.....64189.....1012315......16031147........253594307

..21...876...21489....588529....16031147.....437241277......11938414614

..37..2735..113466...5400933...253594307...11938414614.....563330031268

..65..8583..598374..49414072..4003959566..325438086413...26515589323171

.114.26900.3155426.452274232.63279327977.8875686431050.1248681784524804

Links

R. H. Hardin, Table of n, a(n) for n = 1..241

Formula

Empirical for column k:

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

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

k=3: [order 18]

k=4: [order 45]

Example

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

Crossrefs

Column 1 is A005251(n+2).

Sequence in context: A296386 A296643 A295040 * A220259 A220323 A295416

Adjacent sequences: A295528 A295529 A295530 * A295532 A295533 A295534

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 23 2017

Status

approved