A233257 Number of 2 X n 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

3, 10, 104, 1184, 13952, 166400, 1992704, 23896064, 286687232, 3439984640, 41278767104, 495341010944, 5944075354112, 71328837140480, 855945777250304, 10271348253261824, 123256174744174592, 1479074079750225920

Offset

1,1

Links

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

Formula

Empirical: a(n) = 16*a(n-1) - 48*a(n-2) for n>3.

Conjectures from Colin Barker, Oct 11 2018: (Start)

G.f.: x*(3 - 38*x + 88*x^2) / ((1 - 4*x)*(1 - 12*x)).

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

(End)

Example

Some solutions for n=5:
..0..1..2..5..3....0..1..2..4..3....0..1..5..4..2....0..1..2..1..0
..0..4..2..1..2....5..1..5..4..2....2..4..3..1..2....2..1..5..4..0

Crossrefs

Row 2 of A233256.

Sequence in context: A025541 A203903 A173325 * A261127 A083108 A117664

Adjacent sequences: A233254 A233255 A233256 * A233258 A233259 A233260

Keyword

nonn

Author

R. H. Hardin, Dec 06 2013

Status

approved