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A188152 Number of 7-step self-avoiding walks on an n X n square summed over all starting positions. 1
0, 0, 112, 1248, 4152, 8752, 14932, 22672, 31972, 42832, 55252, 69232, 84772, 101872, 120532, 140752, 162532, 185872, 210772, 237232, 265252, 294832, 325972, 358672, 392932, 428752, 466132, 505072, 545572, 587632, 631252, 676432, 723172, 771472 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Row 7 of A188147.

LINKS

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

FORMULA

Empirical: a(n) = 780*n^2 - 3960*n + 4432 for n>5.

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

G.f.: 4*x^3*(28 + 228*x + 186*x^2 - 18*x^3 - 29*x^4 - 5*x^5) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.

(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: A232785 A232850 A233115 * A327633 A210300 A210293

Adjacent sequences:  A188149 A188150 A188151 * A188153 A188154 A188155

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 22 2011

STATUS

approved

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Last modified January 20 01:01 EST 2022. Contains 350467 sequences. (Running on oeis4.)