A233020 Number of n X 2 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, vertically, diagonally or antidiagonally, and top left element zero.

3, 15, 81, 435, 2337, 12555, 67449, 362355, 1946673, 10458075, 56183721, 301834755, 1621541217, 8711375595, 46799960409, 251422553235, 1350712686993, 7256408541435, 38983468081161, 209430157488675, 1125117723605697

Offset

1,1

Links

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

Formula

Empirical: a(n) = 5*a(n-1) + 2*a(n-2).

Conjectures from Colin Barker, Oct 06 2018: (Start)

G.f.: 3*x / (1 - 5*x - 2*x^2).

a(n) = sqrt(3/11)*(((5+sqrt(33))/2)^n - ((5-sqrt(33))/2)^n) = 3*A015535(n).

(End)

Example

Some solutions for n=5:
..0..2....0..0....0..0....0..1....0..0....0..0....0..1....0..2....0..0....0..0
..2..2....1..1....2..2....1..1....1..1....0..2....0..1....2..0....1..1....0..0
..3..2....1..1....2..3....0..0....0..0....2..2....0..1....2..0....1..1....1..1
..3..2....1..3....3..3....2..2....1..1....2..3....0..1....0..2....3..3....3..1
..2..3....3..3....3..2....0..0....3..1....2..3....0..1....0..2....2..3....3..1

Crossrefs

Column 2 of A233026.

Sequence in context: A003448 A229841 A198628 * A246020 A084120 A163470

Adjacent sequences: A233017 A233018 A233019 * A233021 A233022 A233023

Keyword

nonn

Author

R. H. Hardin, Dec 03 2013

Status

approved