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A266087
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Alternating sum of 11-gonal (or hendecagonal) numbers.
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1
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0, -1, 10, -20, 38, -57, 84, -112, 148, -185, 230, -276, 330, -385, 448, -512, 584, -657, 738, -820, 910, -1001, 1100, -1200, 1308, -1417, 1534, -1652, 1778, -1905, 2040, -2176, 2320, -2465, 2618, -2772, 2934, -3097, 3268, -3440, 3620, -3801, 3990, -4180
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: -x*(1 - 8*x)/((1 - x)*(1 + x)^3).
a(n) = ((18*n^2 + 4*n - 7)*(-1)^n + 7)/8.
a(n) = Sum_{k = 0..n} (-1)^k*A051682(k).
Lim_{n -> infinity} a(n + 1)/a(n) = -1.
E.g.f.: (1/4)*(9*x^2 - 11*x)*cosh(x) - (1/4)*(9*x^2 - 11*x - 7)*sinh(x). - G. C. Greubel, Jan 27 2016
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MATHEMATICA
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Table[((18 n^2 + 4 n - 7) (-1)^n + 7)/8, {n, 0, 43}]
CoefficientList[Series[(x - 8 x^2)/(x^4 + 2 x^3 - 2 x - 1), {x, 0, 50}], x] (* Vincenzo Librandi, Dec 21 2015 *)
Accumulate[Times@@@Partition[Riffle[PolygonalNumber[11, Range[0, 50]], {1, -1}, {2, -1, 2}], 2]] (* Requires Mathematica version 10 or later *) (* or *) LinearRecurrence[{-2, 0, 2, 1}, {0, -1, 10, -20}, 50] (* Harvey P. Dale, Aug 27 2019 *)
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PROG
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(Magma) [(18*(-1)^n*n^2 + 4*(-1)^n*n - 7*(-1)^n + 7)/8: n in [0..50]]; // Vincenzo Librandi, Dec 21 2015
(PARI) x='x+O('x^100); concat(0, Vec(-x*(1-8*x)/((1-x)*(1+x)^3))) \\ Altug Alkan, Dec 21 2015
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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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