This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A163952 The number of functions in a finite set for which the sequence of composition powers ends in a length 3 cycle. 3
 0, 0, 0, 2, 32, 480, 7880, 145320, 3009888, 69554240, 1779185360, 49995179520, 1532580072320, 50934256044672, 1825145974743000, 70172455476381440, 2882264153273207360, 125985060813367664640, 5840066736661562391968, 286204501001426735001600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS See A163951 for the cases ending with length 2 cycles and fixed points. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..387 FORMULA a(n) ~ (2*exp(4/3)-exp(1)) * n^(n-1). - Vaclav Kotesovec, Aug 18 2017 EXAMPLE Any period 3 permutation (or disjoint combinations) is one element to be counted. This starts with n=3, where there are only 2 cases: f1:{1,2,3}->{2,3,1} and f2:{1,2,3}->{3,1,2} but for n>3 there are other elements (non-permutations) to be counted (for instance, with n=5, we count with f:{1,2,3,4,5}->{2,4,5,3,4}). MAPLE b:= proc(n, m) option remember; `if`(m>3, 0, `if`(n=0, x^m, add(       (j-1)!*b(n-j, ilcm(m, j))*binomial(n-1, j-1), j=1..n)))     end: a:= n-> coeff(add(b(j, 1)*n^(n-j)*binomial(n-1, j-1), j=0..n), x, 3): seq(a(n), n=0..25);  # Alois P. Heinz, Aug 14 2017 CROSSREFS Cf. A163951, A163947, A163859. Column k=3 of A222029. Sequence in context: A109772 A230131 A115418 * A246213 A022028 A013776 Adjacent sequences:  A163949 A163950 A163951 * A163953 A163954 A163955 KEYWORD nonn AUTHOR Carlos Alves, Aug 07 2009 EXTENSIONS a(0), a(8)-a(19) from Alois P. Heinz, Aug 14 2017 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 August 18 04:50 EDT 2019. Contains 326072 sequences. (Running on oeis4.)