A208044 Number of n X 3 0..3 arrays with new values 0..3 introduced in row major order and no element equal to any horizontal, vertical or antidiagonal neighbor (colorings ignoring permutations of colors).

2, 8, 44, 244, 1356, 7540, 41932, 233204, 1296972, 7213172, 40116428, 223109620, 1240835916, 6900974452, 38380133836, 213453141236, 1187130917964, 6602291295860, 36718991727308, 204214611724276, 1135750348251468

Offset

1,1

Comments

Column 3 of A208050.

Links

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

Formula

Empirical: a(n) = 7*a(n-1) - 8*a(n-2) for n>3.

Conjectures from Colin Barker, Mar 06 2018: (Start)

G.f.: 2*x*(1 - x)*(1 - 2*x) / (1 - 7*x + 8*x^2).

a(n) = (2^(-5-n)*((7-sqrt(17))^n*(-13+5*sqrt(17)) + (7+sqrt(17))^n*(13+5*sqrt(17)))) / sqrt(17) for n>1.

(End)

Example

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

Crossrefs

Cf. A208050.

Sequence in context: A018986 A192469 A128656 * A362413 A362408 A291697

Adjacent sequences: A208041 A208042 A208043 * A208045 A208046 A208047

Keyword

nonn

Author

R. H. Hardin, Feb 22 2012

Status

approved