A297300 Number of 3 X n 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 2 neighboring 1s.

1, 1, 3, 5, 9, 17, 32, 60, 113, 213, 401, 755, 1422, 2678, 5043, 9497, 17885, 33681, 63428, 119448, 224945, 423617, 797757, 1502339, 2829210, 5327978, 10033667, 18895437, 35583953, 67011825, 126196904, 237654452, 447551697, 842830925

Offset

1,3

Links

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

Formula

Empirical: a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3) - a(n-4) for n>6.

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

Example

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

Crossrefs

Row 3 of A297299.

Sequence in context: A074858 A074860 A374518 * A364543 A213005 A171856

Adjacent sequences: A297297 A297298 A297299 * A297301 A297302 A297303

Keyword

nonn

Author

R. H. Hardin, Dec 27 2017

Status

approved