A295208 Number of n X 3 0..1 arrays with each 1 horizontally or vertically adjacent to 2 or 3 1's.

1, 4, 10, 27, 102, 345, 1162, 4072, 14224, 49604, 173594, 607485, 2125150, 7436416, 26022865, 91060814, 318652127, 1115077417, 3902040209, 13654599697, 47782246634, 167206840944, 585115414586, 2047524354146, 7165006769433

Offset

1,2

Comments

Column 3 of A295213.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Robert Israel, Maple-assisted proof of formula

Formula

Empirical: a(n) = 5*a(n-1) -7*a(n-2) +10*a(n-3) -18*a(n-4) +18*a(n-5) -5*a(n-6) -15*a(n-7) +7*a(n-8) -9*a(n-9) +10*a(n-10) -2*a(n-11) +a(n-12).

Empirical formula confirmed by Robert Israel, Nov 17 2017 (see link).

Example

Some solutions for n=7
..1..1..1. .0..1..1. .0..1..1. .1..1..1. .0..1..1. .0..1..1. .1..1..0
..1..1..1. .0..1..1. .0..1..1. .1..0..1. .0..1..1. .0..1..1. .1..1..0
..1..0..1. .0..0..0. .0..1..0. .1..1..1. .0..1..1. .1..1..1. .1..0..0
..1..0..1. .1..1..0. .0..1..0. .1..1..0. .0..0..0. .1..0..1. .1..0..0
..1..1..1. .1..1..0. .1..1..0. .0..0..0. .0..0..0. .1..0..1. .1..1..0
..0..1..1. .1..1..0. .1..1..0. .1..1..1. .0..1..1. .1..1..1. .1..1..0
..0..0..0. .0..0..0. .1..1..0. .1..1..1. .0..1..1. .0..1..1. .0..0..0

Crossrefs

Cf. A295213.

Sequence in context: A000495 A027067 A050262 * A222453 A186278 A367437

Adjacent sequences: A295205 A295206 A295207 * A295209 A295210 A295211

Keyword

nonn

Author

R. H. Hardin, Nov 17 2017

Status

approved