A296322 Number of n X 3 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 2 neighboring 1s.

1, 5, 11, 23, 54, 122, 278, 634, 1438, 3274, 7451, 16943, 38547, 87691, 199477, 453789, 1032300, 2348324, 5342108, 12152500, 27645148, 62888676, 143062485, 325446157, 740342261, 1684169937, 3831239423, 8715507347, 19826499874, 45102377086

Offset

1,2

Links

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

Formula

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

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

Example

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

Crossrefs

Column 3 of A296327.

Sequence in context: A132177 A340340 A046138 * A097279 A106171 A276174

Adjacent sequences: A296319 A296320 A296321 * A296323 A296324 A296325

Keyword

nonn

Author

R. H. Hardin, Dec 10 2017

Status

approved