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

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) = 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

• S. Janson, On the traveling fly problem.

Crossrefs

Cf. A004734.

Programs

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

Formula

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