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A004734
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Numerator of average distance traveled by n-dimensional fly.
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1
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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
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OFFSET
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1,2
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COMMENTS
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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
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REFERENCES
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S. Janson, On the traveling fly problem, Graph Theory Notes of New York, Vol. XXXI, 17, 1996.
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LINKS
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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