A004734 Numerator of average distance traveled by n-dimensional fly.

1, 8, 3, 32, 5, 64, 35, 512, 63, 1024, 231, 4096, 429, 8192, 6435, 131072, 12155, 262144, 46189, 1048576, 88179, 2097152, 676039, 16777216, 1300075, 33554432, 5014575, 134217728, 9694845, 268435456, 300540195

Offset

1,2

Comments

The average distance is actually d(n) = 2*n!!/(n+1)!! if n is odd, and d(n) = (1*Pi)*4*n!!/(n+1)!! if n is even. So a(n) = numerator(d(n)) if n is odd and a(n) = numerator(Pi*d(n)) if n is even. - Michel Marcus, May 24 2013

References

S. Janson, On the traveling fly problem, Graph Theory Notes of New York, Vol. XXXI, 17, 1996.

Links

Table of n, a(n) for n=1..31.

S. Janson, On the traveling fly problem.

Prog

(PARI) a(n) = {if (n % 2, eo = 2, eo = 4); numerator(eo*prod(i=0, floor((n-1)/2), n-2*i)/prod(i=0, floor(n/2), n+1-2*i)); } \\ Michel Marcus, May 24 2013

Crossrefs

Cf. A004735.

Sequence in context: A213838 A248294 A370564 * A287645 A182054 A302214

Adjacent sequences: A004731 A004732 A004733 * A004735 A004736 A004737

Keyword

nonn,frac

Author

N. J. A. Sloane

Status

approved