A233175 Number of 2 X n 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally, diagonally 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, 8, 80, 800, 8576, 92672, 1009664, 11018240, 120356864, 1315045376, 14370209792, 157036838912, 1716116258816, 18754008252416, 204947383648256, 2239705722650624, 24475955615498240, 267478202279002112

Offset

1,1

Links

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

Formula

Empirical: a(n) = 12*a(n-1) - 128*a(n-3) for n>4.

Conjectures from Colin Barker, Oct 10 2018: (Start)

G.f.: x*(3 - 28*x - 16*x^2 + 224*x^3) / ((1 - 4*x)*(1 - 8*x - 32*x^2)).

a(n) = 2^(2*n-3) + (1/32)*sqrt(3)*(-(4-4*sqrt(3))^n + (4*(1+sqrt(3)))^n) for n>1.

(End)

Example

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

Crossrefs

Row 2 of A233174.

Sequence in context: A376941 A347641 A287389 * A347920 A367273 A070901

Adjacent sequences: A233172 A233173 A233174 * A233176 A233177 A233178

Keyword

nonn

Author

R. H. Hardin, Dec 05 2013

Status

approved