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A291681
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First differences of A067046.
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1
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1, 8, 0, 25, -7, 56, -24, 105, -55, 176, -104, 273, -175, 400, -272, 561, -399, 760, -560, 1001, -759, 1288, -1000, 1625, -1287, 2016, -1624, 2465, -2015, 2976, -2464, 3553, -2975, 4200, -3552, 4921, -4199, 5720, -4920, 6601, -5719, 7568, -6600, 8625, -7567, 9776, -8624
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listen;
history;
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internal format)
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OFFSET
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1,2
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COMMENTS
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a(2n) > 0 and a(2n+1) < 0 for all n >= 2.
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LINKS
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FORMULA
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G.f.: -x*(x^6+x^5-3*x^4-2*x^3+5*x^2+9*x+1)/((x-1)^3*(x+1)^4). - Alois P. Heinz, Sep 04 2017
a(n) = (n^3 + 9*n^2 + 20*n + 12) / 12 for n even.
a(n) = (-n^3 + 7*n + 6) / 12 for n odd.
(End)
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MAPLE
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a:= n-> `if`(irem(n-1, 2, 'r')=0, -(r-1)*(2*r+3)*(r+1)/3
, (2*r+3)*(r+4)*(r+2)/3):
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PROG
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(PARI) Vec(x*(1 + 9*x + 5*x^2 - 2*x^3 - 3*x^4 + x^5 + x^6) / ((1 - x)^3*(1 + x)^4) + O(x^60)) \\ Colin Barker, Sep 29 2017
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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