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A187168 Number of 7-step self-avoiding walks on a n X n X n cube summed over all starting positions. 2
0, 192, 25344, 177120, 568248, 1298016, 2466510, 4175136, 6525450, 9619008, 13557366, 18442080, 24374706, 31456800, 39789918, 49475616, 60615450, 73310976, 87663750, 103775328, 121747266, 141681120, 163678446, 187840800, 214269738 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row 7 of A187162.

LINKS

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

FORMULA

Empirical: a(n) = 16926*n^3 - 85380*n^2 + 128832*n - 57312 for n>5.

Conjectures from Colin Barker, Apr 21 2018: (Start)

G.f.: 6*x^2*(32 + 4096*x + 12816*x^2 + 1844*x^3 - 2240*x^4 + 133*x^5 + 220*x^6 + 25*x^7) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>9.

(End)

EXAMPLE

A solution for 3 X 3 X 3:

..0..0..0.....0..0..0.....0..0..0

..0..0..0.....1..2..0.....0..0..0

..7..0..0.....6..3..0.....5..4..0

CROSSREFS

Cf. A187162.

Sequence in context: A199007 A199006 A001290 * A078272 A299993 A208444

Adjacent sequences:  A187165 A187166 A187167 * A187169 A187170 A187171

KEYWORD

nonn,walk

AUTHOR

R. H. Hardin, Mar 06 2011

STATUS

approved

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Last modified December 1 02:46 EST 2021. Contains 349426 sequences. (Running on oeis4.)