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A187164
Number of 3-step self-avoiding walks on an 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
OFFSET
1,2
COMMENTS
Row 3 of A187162.
LINKS
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: A211755 A211504 A211766 * A110275 A348120 A160335
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 06 2011
STATUS
approved