A208502 Number of 4 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 0 and 1 1 1 vertically.

9, 81, 126, 324, 828, 2124, 5436, 13932, 35676, 91404, 234108, 599724, 1536156, 3935052, 10079676, 25819884, 66138588, 169418124, 433972476, 1111644972, 2847534876, 7294114764, 18684254268, 47860713324, 122597730396, 314040583692

Offset

1,1

Comments

Row 4 of A208501.

Links

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

Formula

Empirical: a(n) = a(n-1) + 4*a(n-2) for n>4.

Conjectures from Colin Barker, Jul 03 2018: (Start)

G.f.: 9*x*(1 + 8*x + x^2 - 14*x^3) / (1 - x - 4*x^2).

a(n) = (9*2^(-6-n)*((1-sqrt(17))^n*(-109+27*sqrt(17)) + (1+sqrt(17))^n*(109+27*sqrt(17)))) / sqrt(17) for n>2.

(End)

Example

Some solutions for n=4:
..0..1..0..0....1..1..1..0....1..0..1..0....1..0..1..1....1..1..0..0
..0..1..1..0....0..1..0..1....1..1..0..1....1..0..1..1....1..0..1..0
..1..0..1..0....1..0..1..1....0..1..1..1....0..1..0..0....0..1..1..0
..1..1..0..1....1..1..1..0....1..0..1..0....1..1..1..1....0..1..0..1

Crossrefs

Cf. A208501.

Sequence in context: A209220 A207689 A209225 * A175370 A207695 A158028

Adjacent sequences: A208499 A208500 A208501 * A208503 A208504 A208505

Keyword

nonn

Author

R. H. Hardin, Feb 27 2012

Status

approved