A063888 Number of n-step walks on a cube lattice starting from the origin but not returning to it at any stage.

1, 6, 30, 180, 1026, 6156, 35940, 215640, 1271106, 7626636, 45182124, 271092744, 1610875836, 9665255016, 57546367704, 345278206224, 2058613385346, 12351680312076, 73717606430364, 442305638582184, 2641804748619732

Offset

0,2

Comments

a(n)/6^n tends to 0.65946...

References

Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 322-331.

Links

Table of n, a(n) for n=0..20.

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

Adjacent sequences: A063885 A063886 A063887 * A063889 A063890 A063891

Keyword

nonn

Author

Henry Bottomley, Aug 28 2001

Status

approved