A188152 Number of 7-step self-avoiding walks on an n X n square summed over all starting positions.
0, 0, 112, 1248, 4152, 8752, 14932, 22672, 31972, 42832, 55252, 69232, 84772, 101872, 120532, 140752, 162532, 185872, 210772, 237232, 265252, 294832, 325972, 358672, 392932, 428752, 466132, 505072, 545572, 587632, 631252, 676432, 723172, 771472
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) = 780*n^2 - 3960*n + 4432 for n>5.
Conjectures from Colin Barker, Apr 27 2018: (Start)
G.f.: 4*x^3*(28 + 228*x + 186*x^2 - 18*x^3 - 29*x^4 - 5*x^5) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.
(End)
Comments