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

1,3

Comments

Row 5 of A188147.

Links

R. H. Hardin, Table of n, a(n) for n = 1..50

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)

Example

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

Crossrefs

Cf. A188147.

Sequence in context: A185763 A220063 A135441 * A234227 A234220 A234208

Adjacent sequences: A188147 A188148 A188149 * A188151 A188152 A188153

Keyword

nonn

Author

R. H. Hardin, Mar 22 2011

Status

approved