A297315 Number of 2 X n 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 1 or 2 neighboring 1s.

1, 7, 23, 66, 207, 654, 2049, 6422, 20119, 63033, 197551, 619096, 1940007, 6079365, 19051015, 59700283, 187082905, 586262278, 1837172149, 5757153010, 18041210871, 56535805498, 177166451873, 555187134041, 1739791875173, 5451991915452

Offset

1,2

Links

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

Formula

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

Empirical g.f.: x*(1 + x - x^2)*(1 + 3*x + 2*x^2 + 4*x^3 - x^5 - x^6) / ((1 - x + 2*x^2 - x^3)*(1 - 2*x - 2*x^2 - 5*x^3 + x^5 + x^6)). - Colin Barker, Feb 26 2019

Example

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

Crossrefs

Row 2 of A297314.

Sequence in context: A066187 A259214 A114246 * A048457 A048458 A134350

Adjacent sequences: A297312 A297313 A297314 * A297316 A297317 A297318

Keyword

nonn

Author

R. H. Hardin, Dec 28 2017

Status

approved