A297520 Number of 2 X n 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 3 neighboring 1s.

1, 5, 17, 33, 65, 193, 529, 1185, 2737, 7169, 18257, 43425, 104945, 264001, 656785, 1597665, 3913009, 9708161, 23980241, 58804257, 144593009, 357011905, 879991825, 2164014945, 5327178673, 13131288833, 32347250513, 79624144545, 196075443953

Offset

1,2

Links

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

Formula

Empirical: a(n) = a(n-1) + 4*a(n-3) + 12*a(n-4).

Empirical g.f.: x*(1 + 4*x + 12*x^2 + 12*x^3) / (1 - x - 4*x^3 - 12*x^4). - Colin Barker, Mar 01 2019

Example

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

Crossrefs

Row 2 of A297519.

Sequence in context: A078654 A083364 A273499 * A026394 A004538 A146231

Adjacent sequences: A297517 A297518 A297519 * A297521 A297522 A297523

Keyword

nonn

Author

R. H. Hardin, Dec 31 2017

Status

approved