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A187164 Number of 3-step self-avoiding walks on a n X n X n cube summed over all starting positions. 2
0, 48, 342, 1056, 2370, 4464, 7518, 11712, 17226, 24240, 32934, 43488, 56082, 70896, 88110, 107904, 130458, 155952, 184566, 216480, 251874, 290928, 333822, 380736, 431850, 487344, 547398, 612192, 681906, 756720, 836814, 922368, 1013562, 1110576 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row 3 of A187162.

LINKS

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

FORMULA

Empirical: a(n) = 30*n^3 - 60*n^2 + 24*n for n>1.

Conjectures from Colin Barker, Apr 20 2018: (Start)

G.f.: 6*x^2*(8 + 25*x - 4*x^2 + x^3) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>5.

(End)

EXAMPLE

A solution for 2 X 2 X 2:

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

..1..2.....0..3

CROSSREFS

Cf. A187162.

Sequence in context: A211504 A211766 A037056 * A110275 A160335 A019558

Adjacent sequences:  A187161 A187162 A187163 * A187165 A187166 A187167

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 06 2011

STATUS

approved

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Last modified October 22 08:00 EDT 2019. Contains 328315 sequences. (Running on oeis4.)