A188153 Number of 8-step self-avoiding walks on an n X n square summed over all starting positions.

0, 0, 112, 1976, 8160, 19312, 35024, 55104, 79528, 108296, 141408, 178864, 220664, 266808, 317296, 372128, 431304, 494824, 562688, 634896, 711448, 792344, 877584, 967168, 1061096, 1159368, 1261984, 1368944, 1480248, 1595896, 1715888, 1840224

Offset

1,3

Comments

Row 8 of A188147.

Links

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

Formula

Empirical: a(n) = 2172*n^2 - 12500*n + 16096 for n>6.

Conjectures from Colin Barker, Apr 27 2018: (Start)

G.f.: 8*x^3*(2 + x)*(7 + 99*x + 111*x^2 - 15*x^3 - 18*x^4 - 3*x^5) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>9.

(End)

Example

Some solutions for 4 X 4:
  0 0 0 0    0 7 8 0    1 4 5 0    6 7 8 0    6 7 0 0
  8 7 6 1    0 6 3 2    2 3 6 7    5 4 0 0    5 8 0 0
  0 0 5 2    0 5 4 1    0 0 0 8    0 3 0 0    4 0 0 0
  0 0 4 3    0 0 0 0    0 0 0 0    1 2 0 0    3 2 1 0

Crossrefs

Cf. A188147.

Sequence in context: A203915 A233884 A246895 * A163194 A267327 A008361

Adjacent sequences: A188150 A188151 A188152 * A188154 A188155 A188156

Keyword

nonn

Author

R. H. Hardin, Mar 22 2011

Status

approved