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A208079 revision #10

A208079

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

9, 81, 441, 2601, 15129, 88209, 514089, 2996361, 17464041, 101787921, 593263449, 3457792809, 20153493369, 117463167441, 684625511241, 3990289900041, 23257113888969, 135552393433809, 790057246713849, 4604791086849321

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Row 4 of A208078.

LINKS

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

FORMULA

Empirical: a(n) = 5*a(n-1) + 5*a(n-2) - a(n-3).

Conjectures from Colin Barker, Jan 20 2018: (Start)

G.f.: 9*x*(1 + 4*x - x^2) / ((1 + x)*(1 - 6*x + x^2)).

a(n) = (9/4)*(2*(-1)^n + (3-2*sqrt(2))^n + (3+2*sqrt(2))^n).

(End)

EXAMPLE

Some solutions for n=4:

..1..0..1..0....1..1..0..1....1..1..1..1....0..1..1..0....1..1..1..0

..1..0..1..1....1..0..1..0....0..1..1..0....1..1..0..0....0..1..1..1

..0..1..0..1....1..0..1..1....0..1..1..1....1..0..1..1....1..1..0..1

..1..1..1..0....1..1..0..1....1..1..0..1....0..1..1..1....1..0..1..0

CROSSREFS

Sequence in context: A207742 A207719 A167717 * A223719 A270295 A214618

Adjacent sequences: A208076 A208077 A208078 * A208080 A208081 A208082

KEYWORD

nonn

AUTHOR

R. H. Hardin, Feb 23 2012

STATUS

approved