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

1,3

Comments

Row 6 of A188147.

Links

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

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)

Example

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

Crossrefs

Cf. A188147.

Sequence in context: A297463 A297700 A218070 * A372094 A297643 A224043

Adjacent sequences: A188148 A188149 A188150 * A188152 A188153 A188154

Keyword

nonn

Author

R. H. Hardin, Mar 22 2011

Status

approved