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

Author

Henry Bottomley, Aug 28 2001

Keywords

• nonn

Comments

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

Examples

			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.
		

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).