A221374 Number of n X 2 arrays of occupancy after each element stays put or moves to some horizontal, vertical or antidiagonal neighbor, with no occupancy greater than 2.

3, 19, 139, 1035, 7723, 57643, 430251, 3211435, 23970475, 178918059, 1335462571, 9968028331, 74402376363, 555346897579, 4145165675179, 30939937811115, 230938839788203, 1723750967061163, 12866252377336491, 96035015150447275

Offset

1,1

Comments

Column 2 of A221378.

Links

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

Formula

Empirical: a(n) = 9*a(n-1) - 12*a(n-2) + 4*a(n-3).

Conjectures from Colin Barker, Aug 05 2018: (Start)

G.f.: x*(3 - 2*x)*(1 - 2*x) / ((1 - x)*(1 - 8*x + 4*x^2)).

a(n) = (1 + (4-2*sqrt(3))^n + (2*(2+sqrt(3)))^n) / 3.

(End)

Example

Some solutions for n=3:
..0..2....1..2....0..2....1..1....2..0....2..2....1..1....0..2....2..1....1..0
..2..2....0..1....2..1....2..1....0..2....1..1....0..0....1..0....0..0....1..0
..0..0....0..2....1..0....1..0....2..0....0..0....2..2....2..1....2..1....2..2

Crossrefs

Cf. A221378.

Sequence in context: A321349 A115750 A156894 * A073515 A074559 A027314

Adjacent sequences: A221371 A221372 A221373 * A221375 A221376 A221377

Keyword

nonn

Author

R. H. Hardin, Jan 13 2013

Status

approved