A229681 Number of defective 3-colorings of an n X 4 0..2 array connected diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.
0, 360, 10896, 186576, 2700432, 35485776, 437924880, 5169543120, 59031049104, 656886585168, 7159989801744, 76729919248080, 810700618461840, 8463178886657616, 87441690785378832, 895373932606109136
Offset: 1
Keywords
Examples
Some solutions for n=3: 0 1 1 0 0 0 1 2 0 1 0 2 0 0 0 1 0 1 1 0 2 2 0 1 1 1 1 1 2 1 2 2 0 2 2 2 0 0 0 2 1 1 0 1 2 2 2 0 2 1 1 0 1 1 1 2 2 2 1 2
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Formula
Empirical: a(n) = 27*a(n-1) - 243*a(n-2) + 729*a(n-3) for n > 6.
Conjectures from Colin Barker, Jun 16 2017: (Start)
G.f.: 24*x^2*(15 + 49*x - 839*x^2 + 2007*x^3 - 1296*x^4) / (1 - 9*x)^3.
a(n) = 16*3^(2*n-7)*(-449 + 60*n + 256*n^2) for n > 3.
(End)
Comments