A375625 Number of distinct values taken by F(p) = Sum (|i-j| - |p(i)-p(j)|)^2 where the sum is over all 1 <= i < j <= n, for all permutations p in the symmetric group S_n.
1, 1, 1, 2, 4, 10, 17, 51, 55, 160, 140, 389, 300, 795, 566, 1290
Offset: 0
Programs
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Maple
F:= S-> add(add((j-i-abs(S[j]-S[i]))^2, i=1..j-1), j=2..nops(S)): a:= n-> nops({map(F, combinat[permute](n))[]}): seq(a(n), n=0..10);
Extensions
a(11)-a(13) from Hugo Pfoertner, Aug 24 2024
a(14)-a(15) from Hugo Pfoertner, Sep 04 2024
Comments