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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 16 17:25 EST 2019. Contains 329201 sequences. (Running on oeis4.)