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Search: id:A064842
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| A064842 |
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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}. |
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+0
2
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| 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
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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K. Selkirk, Re-designing the dartboard, Math. Gaz., 60 (1976), 171-178.
V. Mihai, Problem 10725, Amer. Math. Monthly, 108 (March 2001), pp. 272-273.
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LINKS
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G. L. Cohen and E. Tonkes, Dartboard arrangements, Elect. J. Combin., 8 (No. 2, 2001), #R4.
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FORMULA
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If n mod 2 = 0 then n^3/3-4*n/3+2 else n^3/3-4*n/3+1.
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EXAMPLE
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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).
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MAPLE
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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); (Deutsch)
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CROSSREFS
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Cf. A064843.
Sequence in context: A066286 A034881 A146345 this_sequence A101695 A014741 A016059
Adjacent sequences: A064839 A064840 A064841 this_sequence A064843 A064844 A064845
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Oct 25 2001
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EXTENSIONS
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Edited by Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 30 2005
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