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A239773 Number of pairs of functions f, g from a size n set into itself satisfying f(g(f(x))) = f(f(f(x))). 13
1, 1, 10, 231, 9880, 644845, 58790736, 7077540295 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..7.

MAPLE

s:= proc(n, i) option remember; `if`(i=0, [[]],

       map(x-> seq([j, x[]], j=1..n), s(n, i-1)))

    end:

a:= proc(n) (l-> add(add(`if`([true$n]=[seq(evalb(

       f[g[f[i]]]=f[f[f[i]]]), i=1..n)], 1, 0), g=l), f=l))(s(n$2))

    end:

seq(a(n), n=0..5); # Alois P. Heinz, Jul 16 2014

MATHEMATICA

a[n_] := a[n] = If[n == 0, 1, Module[{f, g, T}, T = Tuples[Range[n], n]; Table[f = T[[j, #]] &; g = T[[k, #]] &; Table[True, {n}] == Table[f[g[f[i]]] == f[f[f[i]]], {i, n}], {j, n^n}, {k, n^n}] // Flatten // Count[#, True] &]];

Table[Print[n, " ", a[n]]; a[n], {n, 0, 5}] (* Jean-Fran├žois Alcover, Sep 24 2022 *)

CROSSREFS

Cf. A181162.

Sequence in context: A056602 A349731 A239772 * A087434 A297648 A012240

Adjacent sequences:  A239770 A239771 A239772 * A239774 A239775 A239776

KEYWORD

nonn,more,changed

AUTHOR

Chad Brewbaker, Mar 26 2014

EXTENSIONS

a(6)-a(7) from Giovanni Resta, Mar 28 2014

STATUS

approved

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Last modified October 7 17:44 EDT 2022. Contains 357275 sequences. (Running on oeis4.)