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A064842 Maximal value of sum([p(i)-p(i+1)]^2,i=1..n), where p(n+1)=p(1), as p ranges over all permutations of {1,2,...,n}. 2
0, 2, 6, 18, 36, 66, 106, 162, 232, 322, 430, 562, 716, 898, 1106, 1346, 1616, 1922, 2262, 2642, 3060, 3522, 4026, 4578, 5176, 5826, 6526, 7282, 8092, 8962, 9890, 10882, 11936, 13058, 14246, 15506, 16836, 18242, 19722, 21282, 22920, 24642, 26446, 28338, 30316 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..45.

G. L. Cohen and E. Tonkes, Dartboard arrangements, Elect. J. Combin., 8 (No. 2, 2001), #R4.

Vasile Mihai and Michael Woltermann, Problem 10725: The Smoothest and Roughest Permutations, Amer. Math. Monthly, 108 (March 2001), pp. 272-273.

K. Selkirk, Re-designing the dartboard, Math. Gaz., 60 (1976), 171-178.

Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1)

FORMULA

If n mod 2 = 0 then n^3/3-4*n/3+2 else n^3/3-4*n/3+1.

G.f. -2*x^2*(-1+x^3-2*x^2) / ( (1+x)*(x-1)^4 ). - R. J. Mathar, Nov 26 2012

a(n) = (2*n^3 - 8*n + 3*(-1)^n + 9)/6. - Luce ETIENNE, Jul 08 2014

EXAMPLE

a(4)=18 because the values of the sum for the permutations of {1,2,3,4} are 10 (8 times), 12 (8 times) and 18 (8 times).

MAPLE

a:=proc(n) if n mod 2 = 0 then (n^3-4*n)/3+2 else (n^3-4*n)/3+1 fi end: seq(a(n), n=1..41); # Emeric Deutsch

CROSSREFS

Cf. A064843.

Sequence in context: A277324 A034881 A146345 * A302647 A324580 A101695

Adjacent sequences:  A064839 A064840 A064841 * A064843 A064844 A064845

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Oct 25 2001

EXTENSIONS

Edited by Emeric Deutsch, Jul 30 2005

STATUS

approved

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Last modified August 22 16:17 EDT 2019. Contains 326178 sequences. (Running on oeis4.)