The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A091160 Number of orbits of length n under the map whose periodic points are counted by A061687. 1
 1, 16, 2835, 2370752, 6611343125, 48887897438124, 821067869874486556, 28006755051982013513984, 1782755223314276717178818904, 198173677662343700104263938337400, 36467946245662764068249155883368682252, 10631160782054640951386529213624176084501136 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..100 Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1. J.-M. Sixdeniers, K. A. Penson and A. I. Solomon, Extended Bell and Stirling Numbers From Hypergeometric Exponentiation, J. Integer Seqs. Vol. 4 (2001), #01.1.4. Thomas Ward, Exactly realizable sequences. [local copy]. FORMULA If b(n) is the (n+1)th term of A061687, then a(n) = (1/n)*Sum_{d|n} mu(d)*b(n/d). EXAMPLE b(1)=1, b(3)=8506, so a(3) = (1/3)*(8506-1) = 2835. MAPLE 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: seq(a(n), n=1..15);  # Alois P. Heinz, Mar 19 2014 MATHEMATICA 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; Array[a, 15] (* Jean-François Alcover, Nov 18 2020, after Alois P. Heinz *) CROSSREFS Cf. A061687. Sequence in context: A016876 A221253 A123282 * A049030 A223068 A051551 Adjacent sequences:  A091157 A091158 A091159 * A091161 A091162 A091163 KEYWORD nonn AUTHOR Thomas Ward, Feb 24 2004 EXTENSIONS More terms from Alois P. Heinz, Mar 19 2014 Name clarified by Michel Marcus, May 13 2015 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 28 04:43 EST 2021. Contains 349400 sequences. (Running on oeis4.)