A102709 Let a(n,m) = card{f^(n) : f is a mapping from a set of m elements into itself}, where f^(l)(x) = f^(l-1)(f(x)),l>0, f^(0)(x) = x; sequence gives a(n,5).

1, 3125, 1075, 985, 580, 1281, 295, 1305, 580, 925, 631, 1305, 220, 1305, 655, 901, 580, 1305, 295, 1305, 556, 925, 655, 1305, 220, 1281, 655, 925, 580, 1305, 271, 1305, 580, 925, 655, 1281, 220, 1305, 655, 925, 556, 1305, 295, 1305, 580, 901, 655, 1305, 220

Offset: 0

Author

Vladeta Jovovic, Feb 05 2005

Keywords

• nonn

Comments

Sequence appears to have a rational o.g.f. - Ralf Stephan, May 18 2007

Links

• Ray Chandler, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (-1, -2, -2, -2, -1, 0, 1, 2, 2, 2, 1, 1).

Crossrefs

Cf. A102687.

Row n=5 of A247026.

Programs

Mathematica

Join[{1, 3125, 1075, 985},LinearRecurrence[{-1, -2, -2, -2, -1, 0, 1, 2, 2, 2, 1, 1},{580, 1281, 295, 1305, 580, 925, 631, 1305, 220, 1305, 655, 901},45]] (* Ray Chandler, Sep 08 2015 *)

Formula

Empirical g.f.: 1+x*(60*x^14 +480*x^13 +2360*x^12 +2584*x^11 +3099*x^10 +2188*x^9 -522*x^8 -4057*x^7 -8367*x^6 -9981*x^5 -12231*x^4 -9965*x^3 -8310*x^2 -4200*x -3125) / ((x -1)*(x +1)*(x^2 -x +1)*(x^2 +1)*(x^2 +x +1)*(x^4 +x^3 +x^2 +x +1)). - Colin Barker, Aug 07 2013

Extensions

a(0) inserted by Alois P. Heinz, Sep 10 2014