A087034 Number of distinct values taken on by f(P)=Sum[p(i)p(n+1-i),i=1..n] as {p(1),p(2),...,p(n)} ranges over all permutations P of {1,2,3,...n}.

1, 1, 2, 3, 8, 9, 34, 35, 103, 77, 207, 138

Offset

1,3

Comments

See A087035 for the maximum value of f(P) as P ranges over all permutations of {1,2,3,...,n}. It appears that the corresponding minimum value of f(P) is given by A000292=C(n+3,3).

Links

Table of n, a(n) for n=1..12.

Example

a(3)=2, since f takes on exactly two distinct values 10 and 13: f({1,2,3})=10, f({1,3,2)}=13, f({2,1,3})=13, f({2,3,1})=13, f({3,1,2})=13 and f({3,2,1})=10.

Crossrefs

Cf. A000292, A087035.

Sequence in context: A119386 A162219 A140484 * A364382 A133165 A019307

Adjacent sequences: A087031 A087032 A087033 * A087035 A087036 A087037

Keyword

nonn

Author

John W. Layman, Jul 31 2003

Status

approved