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A239769 Number of pairs of functions (f, g) from a size n set into itself satisfying f(g(f(x))) = g(g(f(x))). 12
1, 1, 10, 195, 7000, 397445, 32540976, 3612881587 (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]]]=g[g[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]]] == g[g[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 22 2022 *)

CROSSREFS

Cf. A181162, A239773.

Sequence in context: A239766 A294047 A239768 * A152561 A224298 A222499

Adjacent sequences:  A239766 A239767 A239768 * A239770 A239771 A239772

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 4 12:36 EDT 2022. Contains 357239 sequences. (Running on oeis4.)