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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

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Last modified August 18 04:50 EDT 2019. Contains 326072 sequences. (Running on oeis4.)