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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, 1, 2, 4, 10, 17, 51, 55, 160, 140, 389, 300, 795, 566, 1290
OFFSET
0,4
COMMENTS
The function F was defined by Dan Asimov on the Mailing list Math-Fun on Aug. 18, 2024.
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);
CROSSREFS
Sequence in context: A034455 A057491 A005541 * A045955 A182248 A093695
KEYWORD
nonn,more
AUTHOR
W. Edwin Clark, Aug 21 2024
EXTENSIONS
a(11)-a(13) from Hugo Pfoertner, Aug 24 2024
a(14)-a(15) from Hugo Pfoertner, Sep 04 2024
STATUS
approved