A183586 1/24 the number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock containing exactly three distinct values.

6, 56, 520, 4832, 44896, 417152, 3875968, 36013568, 334620160, 3109124096, 28888434688, 268416966656, 2493996949504, 23172979195904, 215311796961280, 2000570126041088, 18588302571864064, 172713262087405568

Offset

1,1

Comments

Column 1 of A183594.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = 8*a(n-1) + 12*a(n-2).

Conjectures from Colin Barker, Mar 29 2018: (Start)

G.f.: 2*x*(3 + 4*x) / (1 - 8*x - 12*x^2).

a(n) = ((4-2*sqrt(7))^n*(-5+2* sqrt(7)) + (2*(2+sqrt(7)))^n*(5+2*sqrt(7))) / (6*sqrt(7)).

(End)

Example

Some solutions with a(1,1)=0 for 3 X 2:
..0..3....0..1....0..3....0..2....0..1....0..3....0..1....0..2....0..2....0..2
..3..1....2..2....1..0....0..1....1..3....2..3....3..3....3..0....1..1....3..2
..0..3....0..1....0..3....0..3....2..2....2..1....0..2....2..2....2..0....3..0

Crossrefs

Cf. A183594.

Sequence in context: A277975 A347718 A155613 * A166177 A183615 A181589

Adjacent sequences: A183583 A183584 A183585 * A183587 A183588 A183589

Keyword

nonn

Author

R. H. Hardin, Jan 05 2011

Status

approved