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A004735 Denominator of average distance traveled by n-dimensional fly. 2
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,frac
AUTHOR
STATUS
approved

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Last modified March 29 06:57 EDT 2024. Contains 371265 sequences. (Running on oeis4.)