A188151 Number of 6-step self-avoiding walks on an n X n square summed over all starting positions.
0, 0, 128, 800, 2112, 4008, 6472, 9504, 13104, 17272, 22008, 27312, 33184, 39624, 46632, 54208, 62352, 71064, 80344, 90192, 100608, 111592, 123144, 135264, 147952, 161208, 175032, 189424, 204384, 219912, 236008, 252672, 269904, 287704, 306072
Offset: 1
Keywords
Examples
Some solutions for 3 X 3: 5 4 3 0 6 7 2 3 4 6 7 0 0 7 0 7 4 3 1 0 0 6 0 2 4 5 0 1 0 5 5 2 1 1 6 5 6 5 2 2 7 6 7 0 1 3 2 1 0 7 6 4 3 0 2 3 4 0 0 1 3 4 5
Links
- R. H. Hardin, Table of n, a(n) for n = 1..50
Crossrefs
Cf. A188147.
Formula
Empirical: a(n) = 284*n^2 - 1228*n + 1152 for n>4.
Conjectures from Colin Barker, Apr 27 2018: (Start)
G.f.: 8*x^3*(16 + 52*x + 12*x^2 - 7*x^3 - 2*x^4) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>7.
(End)
Comments