A297508 Number of 3 X n 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 2 neighboring 1s.

1, 29, 110, 314, 1829, 8803, 34757, 157673, 735144, 3208028, 14196017, 64154943, 286007061, 1271032033, 5685858000, 25403326244, 113255416409, 505585282497, 2257780807909, 10075966019543, 44971626813134, 200763429520862

Offset

1,2

Links

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

Formula

Empirical: a(n) = 3*a(n-1) + a(n-2) + 32*a(n-3) - 15*a(n-4) - 65*a(n-5) - 74*a(n-6) + 56*a(n-7) + 24*a(n-8) - 3*a(n-9) + 12*a(n-10).

Empirical g.f.: x*(1 + 26*x + 22*x^2 - 77*x^3 - 136*x^4 - 18*x^5 + 80*x^6 + 21*x^7 + 9*x^8 + 12*x^9) / (1 - 3*x - x^2 - 32*x^3 + 15*x^4 + 65*x^5 + 74*x^6 - 56*x^7 - 24*x^8 + 3*x^9 - 12*x^10). - Colin Barker, Feb 28 2019

Example

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

Crossrefs

Row 3 of A297506.

Sequence in context: A044661 A010017 A256648 * A232780 A232787 A232852

Adjacent sequences: A297505 A297506 A297507 * A297509 A297510 A297511

Keyword

nonn

Author

R. H. Hardin, Dec 31 2017

Status

approved