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
Keywords
Examples
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
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Cf. A208050.
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)
Comments