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A063888 Number of n-step walks on a cube lattice starting from the origin but not returning to it at any stage. 0
1, 6, 30, 180, 1026, 6156, 35940, 215640, 1271106, 7626636, 45182124, 271092744, 1610875836, 9665255016, 57546367704, 345278206224, 2058613385346, 12351680312076, 73717606430364, 442305638582184, 2641804748619732 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
a(n)/6^n tends to 0.65946...
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 322-331.
LINKS
Steven R. Finch, Polya's Random Walk Constants [Broken link]
Steven R. Finch, Polya's Random Walk Constants [From the Wayback machine]
FORMULA
a(2n) = 6*a(2n-1)-A049037(n); a(2n+1) = 6*a(2n).
EXAMPLE
a(2) = 30 since there are 36 2-step walks but 6 of them involve a return to the origin at some stage; similarly a(3) = 180 since there are 216 3-step walks but 36 of them involve a return to the origin at some stage.
CROSSREFS
Sequence in context: A057754 A001473 A334288 * A029571 A357599 A368524
KEYWORD
nonn
AUTHOR
Henry Bottomley, Aug 28 2001
STATUS
approved

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Last modified April 22 08:30 EDT 2024. Contains 371893 sequences. (Running on oeis4.)