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

Author

R. H. Hardin, Mar 22 2011

Keywords

• nonn

Comments

Row 8 of A188147.

Examples

			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
		

Links

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

Crossrefs

Cf. A188147.

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)