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

1,3

Comments

Row 7 of A188147.

Links

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

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)

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: A232785 A232850 A233115 * A353782 A367363 A327633

Adjacent sequences: A188149 A188150 A188151 * A188153 A188154 A188155

Keyword

nonn

Author

R. H. Hardin, Mar 22 2011

Status

approved