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

Author

N. J. A. Sloane

Keywords

• nonn
• frac

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

• S. Janson, On the traveling fly problem.

Crossrefs

Cf. A004735.

Programs

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