A230269 Number of n X 2 0..2 arrays x(i,j) with each element horizontally or vertically next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero.

0, 0, 2, 8, 30, 108, 386, 1376, 4902, 17460, 62186, 221480, 788814, 2809404, 10005842, 35636336, 126920694, 452034756, 1609945658, 5733906488, 20421610782, 72732645324, 259041157538, 922588763264, 3285848604870, 11702723341140

Offset

1,3

Comments

Column 2 of A230275.

Links

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

Formula

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

Conjectures from Colin Barker, Feb 24 2018: (Start)

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

a(n) = -1/2 + (2^(-2-n)*(-(-5+sqrt(17))*(3+sqrt(17))^n - (3-sqrt(17))^n*(5+sqrt(17)))) / sqrt(17).

(End)

Example

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

Crossrefs

Cf. A230275.

Sequence in context: A168605 A127865 A199923 * A278023 A077839 A052530

Adjacent sequences: A230266 A230267 A230268 * A230270 A230271 A230272

Keyword

nonn

Author

R. H. Hardin, Oct 14 2013

Status

approved