A229600 Number of defective 3-colorings of an n X 2 0..2 array connected horizontally and vertically with exactly two mistakes, and colors introduced in row-major 0..2 order.
0, 6, 39, 202, 925, 3924, 15795, 61182, 230121, 845640, 3049407, 10825650, 37929141, 131403708, 450839115, 1533738726, 5178892545, 17371743408, 57926537559, 192131864730, 634207340493, 2084322230820, 6822862231779, 22252658047182
Offset: 1
Keywords
Examples
Some solutions for n=3: 0 1 0 1 0 1 0 0 0 1 0 1 0 1 0 1 0 1 0 1 1 2 2 0 0 1 0 1 1 2 2 1 2 2 1 1 2 2 2 2 1 2 2 0 2 0 1 2 2 2 2 0 1 1 2 0 0 2 2 0
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Cf. A229606.
Formula
Empirical: a(n) = 9*a(n-1) - 27*a(n-2) + 27*a(n-3) for n>5.
Conjectures from Colin Barker, Mar 16 2018: (Start)
G.f.: x^2*(6 - 15*x + 13*x^2 - 2*x^3) / (1 - 3*x)^3.
a(n) = 3^(n-5) * (31*n+32*n^2-30) for n>2.
(End)
Comments