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A188153
Number of 8-step self-avoiding walks on an n X n square summed over all starting positions.
1
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 22 2011
STATUS
approved