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A240134
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Numerator of (n-1) * ceiling(n/2) / n.
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1
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0, 1, 4, 3, 12, 5, 24, 7, 40, 9, 60, 11, 84, 13, 112, 15, 144, 17, 180, 19, 220, 21, 264, 23, 312, 25, 364, 27, 420, 29, 480, 31, 544, 33, 612, 35, 684, 37, 760, 39, 840, 41, 924, 43, 1012, 45, 1104, 47, 1200, 49, 1300, 51, 1404, 53, 1512, 55, 1624, 57, 1740, 59, 1860, 61, 1984, 63, 2112, 65
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OFFSET
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1,3
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COMMENTS
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LINKS
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FORMULA
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a(2n) = 2n-1. a(2n-1) = 2n(n-1).
a(n) = 3*a(n-2)-3*a(n-4)+a(n-6). G.f.: x^2*(x^4-4*x-1) / ((x-1)^3*(x+1)^3). - Colin Barker, Apr 02 2014
a(n) = n - 1 + (2*floor((n+2)/2)^2 - 2*floor((n+2)/2) - n + 1) * (n mod 2). - Wesley Ivan Hurt, Apr 02 2014
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MAPLE
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MATHEMATICA
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Table[Numerator[(n - 1) Ceiling[n/2] / n], {n, 100}]
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PROG
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(PARI) concat(0, Vec(x^2*(x^4-4*x-1)/((x-1)^3*(x+1)^3) + O(x^100))) \\ Colin Barker, Apr 02 2014
(Magma) [(n-1)*(n+3-(n-1)*(-1)^n)/4 : n in [1..80]]; // Wesley Ivan Hurt, Dec 05 2023
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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