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A091160
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Number of orbits of length n under the map whose periodic points are counted by A061687.
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1
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1, 16, 2835, 2370752, 6611343125, 48887897438124, 821067869874486556, 28006755051982013513984, 1782755223314276717178818904, 198173677662343700104263938337400, 36467946245662764068249155883368682252, 10631160782054640951386529213624176084501136
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OFFSET
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1,2
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COMMENTS
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Old name was: A061687 appears to count the periodic points for a certain map. If so, then this is the sequence of the numbers of orbits of length n for that map.
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LINKS
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FORMULA
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If b(n) is the (n+1)th term of A061687, then a(n) = (1/n)*Sum_{d|n} mu(d)*b(n/d).
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EXAMPLE
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b(1)=1, b(3)=8506, so a(3) = (1/3)*(8506-1) = 2835.
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MAPLE
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with(numtheory):
b:= proc(n) option remember;
`if`(n=0, 1, add(binomial(n, k)^6*(n-k)*b(k)/n, k=0..n-1))
end:
a:= n-> add(mobius(d)*b(n/d), d=divisors(n))/n:
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MATHEMATICA
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b[n_] := b[n] = If[n==0, 1, Sum[Binomial[n, k]^6 (n-k)b[k]/n, {k, 0, n-1}]];
a[n_] := Sum[MoebiusMu[d] b[n/d], {d, Divisors[n]}]/n;
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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