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A187165 Number of 4-step self-avoiding walks on an n X n X n cube summed over all starting positions. 2
0, 96, 1104, 3984, 9612, 18888, 32712, 51984, 77604, 110472, 151488, 201552, 261564, 332424, 415032, 510288, 619092, 742344, 880944, 1035792, 1207788, 1397832, 1606824, 1835664, 2085252, 2356488, 2650272, 2967504, 3309084, 3675912, 4068888 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Row 4 of A187162.
LINKS
FORMULA
Empirical: a(n) = 150*n^3 - 426*n^2 + 312*n - 48 for n>2.
Conjectures from Colin Barker, Apr 20 2018: (Start)
G.f.: 12*x^2*(8 + 60*x + 12*x^2 - 7*x^3 + 2*x^4) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>6.
(End)
EXAMPLE
A solution for 2 X 2 X 2:
..2..0.....3..4
..1..0.....0..0
CROSSREFS
Cf. A187162.
Sequence in context: A027628 A182684 A232918 * A229533 A282017 A263567
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 06 2011
STATUS
approved

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Last modified February 22 03:55 EST 2024. Contains 370239 sequences. (Running on oeis4.)