A295546 Number of n X 3 0..1 arrays with each 1 horizontally or vertically adjacent to 1, 3 or 4 1's.

3, 11, 34, 116, 391, 1304, 4374, 14645, 49051, 164353, 550580, 1844483, 6179157, 20700471, 69348050, 232320799, 778290532, 2607326895, 8734723380, 29261921589, 98029444240, 328405359664, 1100180474788, 3685680030204, 12347280822238

Offset

1,1

Comments

Column 3 of A295551.

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) -6*a(n-2) +2*a(n-3) -3*a(n-4) +12*a(n-5) -24*a(n-6) +a(n-7) +17*a(n-8) -3*a(n-9) +6*a(n-10) +8*a(n-11) +5*a(n-12) -15*a(n-13) +12*a(n-14) -9*a(n-15) +2*a(n-16) -a(n-17).

Empirical formula confirmed by Robert Israel, Nov 23 2017 (see link).

Example

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

Crossrefs

Cf. A295551.

Sequence in context: A355364 A180762 A134326 * A361435 A094308 A166046

Adjacent sequences: A295543 A295544 A295545 * A295547 A295548 A295549

Keyword

nonn

Author

R. H. Hardin, Nov 23 2017

Status

approved