A299590 Number of n X 3 0..1 arrays with every element unequal to 0, 1 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

3, 3, 5, 11, 19, 35, 65, 120, 220, 404, 744, 1369, 2517, 4629, 8515, 15662, 28806, 52982, 97450, 179239, 329671, 606359, 1115269, 2051300, 3772928, 6939496, 12763724, 23476149, 43179369, 79419241, 146074759, 268673370, 494167370, 908915498

Offset

1,1

Comments

Column 3 of A299595.

Links

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

Formula

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

Empirical g.f.: x*(3 + 2*x^2 - x^4 + x^7) / ((1 + x^2)*(1 - x - x^2 - x^3)). - Colin Barker, Feb 15 2018

Example

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

Crossrefs

Cf. A299595.

Sequence in context: A301500 A084656 A073749 * A250396 A201866 A191632

Adjacent sequences: A299587 A299588 A299589 * A299591 A299592 A299593

Keyword

nonn

Author

R. H. Hardin, Feb 13 2018

Status

approved