A004735 Denominator of average distance traveled by n-dimensional fly.

1, 3, 4, 15, 8, 35, 64, 315, 128, 693, 512, 3003, 1024, 6435, 16384, 109395, 32768, 230945, 131072, 969969, 262144, 2028117, 2097152, 16900975, 4194304, 35102025, 16777216, 145422675, 33554432

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) = denominator(d(n)) if n is odd and a(n) = denominator(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..29.

S. Janson, On the traveling fly problem.

Formula

a(2n) = A001803(n) (conjectured). - Ralf Stephan, Mar 10 2004

Prog

(PARI) a(n) = {if (n % 2, eo = 2, eo = 4); denominator(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. A004734.

Sequence in context: A070971 A338438 A130113 * A240673 A066830 A359070

Adjacent sequences: A004732 A004733 A004734 * A004736 A004737 A004738

Keyword

nonn,frac

Author

N. J. A. Sloane

Status

approved