A188150 Number of 5-step self-avoiding walks on an n X n square summed over all starting positions.
0, 0, 104, 432, 972, 1712, 2652, 3792, 5132, 6672, 8412, 10352, 12492, 14832, 17372, 20112, 23052, 26192, 29532, 33072, 36812, 40752, 44892, 49232, 53772, 58512, 63452, 68592, 73932, 79472, 85212, 91152, 97292, 103632, 110172, 116912, 123852, 130992
Offset: 1
Keywords
Examples
Some solutions for 3 X 3: 5 4 3 1 0 5 5 0 1 2 1 0 0 1 0 1 0 0 5 0 0 0 1 2 2 3 4 4 3 2 3 4 5 0 2 3 2 0 0 4 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 4 3 4 5 1 2 0
Links
- R. H. Hardin, Table of n, a(n) for n = 1..50
Crossrefs
Cf. A188147.
Formula
Empirical: a(n) = 100*n^2 - 360*n + 272 for n>3.
Conjectures from Colin Barker, Apr 27 2018: (Start)
G.f.: 4*x^3*(26 + 30*x - 3*x^2 - 3*x^3) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>6.
(End)
Comments