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 A087034 #21 Aug 24 2024 22:56:33
%S A087034 1,1,1,2,3,8,9,34,35,103,77,207,138,351,222,546,334,801,478,1124,658,
%T A087034 1523,878,2006,1142,2581,1454,3256,1818
%N 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}.
%C A087034 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).
%e A087034 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.
%Y A087034 Cf. A000292, A087035.
%K A087034 nonn,more
%O A087034 0,4
%A A087034 _John W. Layman_, Jul 31 2003
%E A087034 a(0)=1 prepended and a(13)-a(28) added by _Alois P. Heinz_, Aug 24 2024