%I A110611
%S A110611 1,4,11,21,37,58,87,123,169,224,291,369,461,566,687,823,977,1148,1339,
%T A110611 1549,1781,2034,2311,2611,2937,3288,3667,4073,4509,4974,5471,5999,6561,
%U A110611 7156,7787,8453,9157,9898,10679,11499,12361,13264,14211,15201,16237
%N A110611 Minimal value of sum(p(i)p(i+1),i=1..n), where p(n+1)=p(1), as p ranges 
               over all permutations of {1,2,...,n}.
%D A110611 The Fifty-Seventh William Lowell Putnam Competition, Amer. Math. Monthly, 
               104, 1997, 744-754, Problem B-3.
%D A110611 V. Mihai, Problem 10725, Amer. Math. Monthly, 108 (March 2001), pp. 272-273.
%F A110611 a(n)=(n^3+3*n^2+5*n-6)/6 if n is even; a(n)=(n^3+3*n^2+5*n-3)/6 if n 
               is odd.
%e A110611 a(4)=21 because the values of the sum for the permutations of {1,2,3,
               4} are 21 (8 times), 24 (8 times) and 25 (8 times).
%p A110611 a:=proc(n) if n mod 2 = 0 then (n^3+3*n^2+5*n-6)/6 else (n^3+3*n^2+5*n-3)/
               6 fi end: seq(a(n),n=1..52);
%Y A110611 Cf. A064842, A110610.
%Y A110611 Sequence in context: A008017 A008205 A008095 this_sequence A008004 A009900 
               A008230
%Y A110611 Adjacent sequences: A110608 A110609 A110610 this_sequence A110612 A110613 
               A110614
%K A110611 nonn
%O A110611 1,2
%A A110611 Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 30 2005