This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A375625 #21 Sep 04 2024 15:52:20
%S A375625 1,1,1,2,4,10,17,51,55,160,140,389,300,795,566,1290
%N 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.
%C A375625 The function F was defined by Dan Asimov on the Mailing list Math-Fun on Aug. 18, 2024.
%p A375625 F:= S-> add(add((j-i-abs(S[j]-S[i]))^2, i=1..j-1), j=2..nops(S)):
%p A375625 a:= n-> nops({map(F, combinat[permute](n))[]}):
%p A375625 seq(a(n), n=0..10);
%Y A375625 Cf. A126972, A375623.
%K A375625 nonn,more
%O A375625 0,4
%A A375625 _W. Edwin Clark_, Aug 21 2024
%E A375625 a(11)-a(13) from _Hugo Pfoertner_, Aug 24 2024
%E A375625 a(14)-a(15) from _Hugo Pfoertner_, Sep 04 2024