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

Author

W. Edwin Clark, Aug 21 2024

Keywords

• nonn
• more

Comments

The function F was defined by Dan Asimov on the Mailing list Math-Fun on Aug. 18, 2024.

Crossrefs

Cf. A126972, A375623.

Programs

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