A232921 Number of 2 X n 0..2 arrays with no element x(i,j) adjacent to value 2-x(i,j) horizontally, diagonally or antidiagonally.

9, 18, 54, 144, 396, 1080, 2952, 8064, 22032, 60192, 164448, 449280, 1227456, 3353472, 9161856, 25030656, 68385024, 186831360, 510432768, 1394528256, 3809922048, 10408900608, 28437645312, 77693091840, 212261474304

Offset

1,1

Links

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

Formula

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

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

G.f.: 9*x / (1 - 2*x - 2*x^2).

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

(End)

Example

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

Crossrefs

Row 2 of A232920.

Sequence in context: A086500 A022669 A107313 * A295473 A255839 A361082

Adjacent sequences: A232918 A232919 A232920 * A232922 A232923 A232924

Keyword

nonn

Author

R. H. Hardin, Dec 02 2013

Status

approved