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

1, 1, 1, 2, 3, 8, 9, 34, 35, 103, 77, 207, 138, 351, 222, 546, 334, 801, 478, 1124, 658, 1523, 878, 2006, 1142, 2581, 1454, 3256, 1818

Offset: 0

Author

John W. Layman, Jul 31 2003

Keywords

• nonn
• more

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+2,3).

Examples

			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.

Extensions

a(0)=1 prepended and a(13)-a(28) added by Alois P. Heinz, Aug 24 2024