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A188151 Number of 6-step self-avoiding walks on an n X n square summed over all starting positions. 1
0, 0, 128, 800, 2112, 4008, 6472, 9504, 13104, 17272, 22008, 27312, 33184, 39624, 46632, 54208, 62352, 71064, 80344, 90192, 100608, 111592, 123144, 135264, 147952, 161208, 175032, 189424, 204384, 219912, 236008, 252672, 269904, 287704, 306072 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Row 6 of A188147.

LINKS

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

FORMULA

Empirical: a(n) = 284*n^2 - 1228*n + 1152 for n>4.

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

G.f.: 8*x^3*(16 + 52*x + 12*x^2 - 7*x^3 - 2*x^4) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>7.

(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: A297463 A297700 A218070 * A297643 A224043 A188841

Adjacent sequences:  A188148 A188149 A188150 * A188152 A188153 A188154

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 22 2011

STATUS

approved

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Last modified May 17 23:07 EDT 2022. Contains 353779 sequences. (Running on oeis4.)