A296390 Number of n X 2 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 1 or 3 neighboring 1's.

2, 6, 11, 28, 63, 139, 328, 735, 1684, 3853, 8750, 20021, 45627, 104068, 237541, 541649, 1235897, 2819380, 6431345, 14672588, 33470945, 76356833, 174191649, 397374570, 906523725, 2068021039, 4717711395, 10762383681, 24551876711

Offset

1,1

Links

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

Formula

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

Empirical g.f.: x*(2 + 4*x + x^2 + x^3 + 3*x^4 - 4*x^5 - 4*x^6 + x^7 + x^8) / (1 - x - 2*x^2 - 2*x^3 + x^4 - 4*x^5 + x^6 + 4*x^7 - x^9). - Colin Barker, Feb 23 2019

Example

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

Crossrefs

Column 2 of A296396.

Sequence in context: A275222 A165821 A365046 * A135048 A189319 A268501

Adjacent sequences: A296387 A296388 A296389 * A296391 A296392 A296393

Keyword

nonn

Author

R. H. Hardin, Dec 11 2017

Status

approved