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A064842
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Maximal value of Sum_{i=1..n} (p(i) - p(i+1))^2, where p(n+1) = p(1), as p ranges over all permutations of {1, 2, ..., n}.
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4
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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, 24642, 26446, 28338, 30316
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OFFSET
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1,2
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LINKS
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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.
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
E.g.f.: (2 - x + x^2 + x^3/3)*cosh(x) + (1 - x + x^2 + x^3/3)*sinh(x) - 2. - Stefano Spezia, Apr 13 2024
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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); # Emeric Deutsch
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MATHEMATICA
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LinearRecurrence[{3, -2, -2, 3, -1}, {0, 2, 6, 18, 36}, 45] (* Jean-François Alcover, Apr 01 2020 *)
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CROSSREFS
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KEYWORD
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nonn,easy,changed
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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