A221304 Number of n X 2 arrays of occupancy after each element moves to some horizontal, vertical or antidiagonal neighbor, with every occupancy equal to zero or two.

0, 5, 10, 31, 90, 259, 746, 2150, 6192, 17831, 51346, 147850, 425724, 1225834, 3529664, 10163285, 29264046, 84262511, 242624302, 698608939, 2011564422, 5792069134, 16677598712, 48021232079, 138271627638, 398137284986

Offset

1,2

Comments

Column 2 of A221308.

Links

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

Formula

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

Empirical g.f.: x^2*(5 - 10*x + 6*x^2 - 4*x^3 + 2*x^4) / ((1 - 3*x + x^3)*(1 - x - x^3)). - Colin Barker, Aug 05 2018

Example

All solutions for n=3:
..0..0....0..2....2..2....0..2....0..2....2..0....0..2....2..0....0..0....0..0
..2..0....2..2....0..2....0..2....0..2....2..0....2..0....2..2....2..2....2..2
..2..2....0..0....0..0....2..0....0..2....2..0....2..0....0..0....2..0....0..2

Crossrefs

Cf. A221308.

Sequence in context: A020995 A174467 A005201 * A094234 A052538 A240413

Adjacent sequences: A221301 A221302 A221303 * A221305 A221306 A221307

Keyword

nonn

Author

R. H. Hardin, Jan 09 2013

Status

approved