A295201 Number of nX4 0..1 arrays with each 1 horizontally or vertically adjacent to 2 or 4 1s.

1, 4, 14, 42, 108, 284, 777, 2146, 5887, 16061, 43813, 119691, 327167, 894141, 2443118, 6675212, 18239201, 49837854, 136179673, 372101538, 1016738643, 2778163068, 7591134970, 20742245392, 56676717731, 154865094839, 423157850846

Offset

1,2

Comments

Column 4 of A295205.

Links

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

Robert Israel, Maple-aided proof of formula

Formula

Empirical: a(n) = 3*a(n-1) -2*a(n-2) +2*a(n-3) +5*a(n-4) -a(n-5) -3*a(n-6) -a(n-7) -6*a(n-8) -10*a(n-9) -a(n-10) +a(n-11) +a(n-12) +a(n-13)

Empirical formula confirmed by Robert Israel, Nov 19 2017 (see link)

Example

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

Crossrefs

Cf. A295205.

Sequence in context: A132357 A262875 A219867 * A309296 A124616 A335514

Adjacent sequences: A295198 A295199 A295200 * A295202 A295203 A295204

Keyword

nonn

Author

R. H. Hardin, Nov 16 2017

Status

approved