Search: id:A110610
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%I A110610
%S A110610 1,4,11,25,48,82,129,191,270,368,487,629,796,990,1213,1467,1754,2076,
%T A110610 2435,2833,3272,3754,4281,4855,5478,6152,6879,7661,8500,9398,10357,
%U A110610 11379,12466,13620,14843,16137,17504,18946,20465,22063,23742,25504
%N A110610 Maximal 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 A110610 The Fifty-Seventh William Lowell Putnam Competition, Amer. Math. Monthly, 
               104, 1997, 744-754, Problem B-3.
%D A110610 V. Mihai, Problem 10725, Amer. Math. Monthly, 108 (March 2001), pp. 272-273.
%F A110610 a(1)=1; a(n)=(2n^3+3n^2-11n+18)/6 for n>=2.
%e A110610 a(4)=25 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 A110610 a:=proc(n) if n=1 then 1 else (2*n^3+3*n^2-11*n+18)/6 fi end: seq(a(n),
               n=1..50);
%Y A110610 Cf. A016825, A110611.
%Y A110610 Sequence in context: A159348 A159349 A115294 this_sequence A051462 A006004 
               A006522
%Y A110610 Adjacent sequences: A110607 A110608 A110609 this_sequence A110611 A110612 
               A110613
%K A110610 nonn
%O A110610 1,2
%A A110610 Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 30 2005

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