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 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}. 4
 1, 4, 11, 25, 48, 82, 129, 191, 270, 368, 487, 629, 796, 990, 1213, 1467, 1754, 2076, 2435, 2833, 3272, 3754, 4281, 4855, 5478, 6152, 6879, 7661, 8500, 9398, 10357, 11379, 12466, 13620, 14843, 16137, 17504, 18946, 20465, 22063, 23742, 25504 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Michael De Vlieger, Table of n, a(n) for n = 1..10000 Leonard F. Klosinski, Gerald L. Alexanderson and Loren C. Larson, The Fifty-Seventh William Lowell Putnam Competition, Amer. Math. Monthly, 104, 1997, 744-754, Problem B-3. Vasile Mihai and Michael Woltermann, Problem 10725: The Smoothest and Roughest Permutations, Amer. Math. Monthly, 108 (March 2001), pp. 272-273. Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA a(1)=1; a(n)=(2n^3+3n^2-11n+18)/6 for n>=2. G.f.: x*(1+x)*(1-x+2*x^2-x^3)/(1-x)^4. [Colin Barker, Jul 24 2012] EXAMPLE 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). MAPLE 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); MATHEMATICA Rest@ CoefficientList[Series[x (1 + x) (1 - x + 2 x^2 - x^3)/(1 - x)^4, {x, 0, 42}], x] (* Michael De Vlieger, Jan 29 2022 *) CROSSREFS Cf. A016825, A110611. Cf. also A064842, A087035, A185173. Sequence in context: A181946 A176959 A115294 * A051462 A006004 A290876 Adjacent sequences: A110607 A110608 A110609 * A110611 A110612 A110613 KEYWORD nonn,easy AUTHOR Emeric Deutsch, Jul 30 2005 STATUS approved

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Last modified December 9 23:05 EST 2022. Contains 358710 sequences. (Running on oeis4.)