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A239773
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Number of pairs of functions f, g from a size n set into itself satisfying f(g(f(x))) = f(f(f(x))).
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13
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OFFSET
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0,3
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LINKS
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MAPLE
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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:
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MATHEMATICA
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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] &]];
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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