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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). 1
3, 8, 80, 800, 8576, 92672, 1009664, 11018240, 120356864, 1315045376, 14370209792, 157036838912, 1716116258816, 18754008252416, 204947383648256, 2239705722650624, 24475955615498240, 267478202279002112 (list; graph; refs; listen; history; text; internal format)
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: A208817 A060752 A287389 * A070901 A079657 A136309

Adjacent sequences:  A233172 A233173 A233174 * A233176 A233177 A233178

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 05 2013

STATUS

approved

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Last modified January 23 20:39 EST 2021. Contains 340386 sequences. (Running on oeis4.)