The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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}. 2
 1, 4, 11, 21, 37, 58, 87, 123, 169, 224, 291, 369, 461, 566, 687, 823, 977, 1148, 1339, 1549, 1781, 2034, 2311, 2611, 2937, 3288, 3667, 4073, 4509, 4974, 5471, 5999, 6561, 7156, 7787, 8453, 9157, 9898, 10679, 11499, 12361, 13264, 14211, 15201, 16237 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 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 (3,-2,-2,3,-1). FORMULA 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. G.f.: x*(1+x+x^2-2*x^3+x^4)/((1-x)^4*(1+x)). [Colin Barker, May 10 2012] a(n) = (2*n^3+6*n^2+10*n-9-3*(-1)^n)/12. - Luce ETIENNE, Jul 26 2014 EXAMPLE 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). MAPLE 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); MATHEMATICA CoefficientList[Series[(1+x+x^2-2*x^3+x^4)/((1-x)^4*(1+x)), {x, 0, 50}], x] (* Vincenzo Librandi, May 11 2012 *) PROG (Magma) I:=[1, 4, 11, 21, 37]; [n le 5 select I[n] else 3*Self(n-1)-2*Self(n-2)-2*Self(n-3)+3*Self(n-4)-Self(n-5): n in [1..50]]; // Vincenzo Librandi, May 11 2012 CROSSREFS Cf. A064842, A110610. Sequence in context: A301239 A301161 A301173 * A008004 A212254 A301064 Adjacent sequences: A110608 A110609 A110610 * A110612 A110613 A110614 KEYWORD nonn,easy AUTHOR Emeric Deutsch, Jul 30 2005 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 1 23:44 EST 2022. Contains 358485 sequences. (Running on oeis4.)