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A266086
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Alternating sum of 9-gonal (or nonagonal) numbers.
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1
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0, -1, 8, -16, 30, -45, 66, -88, 116, -145, 180, -216, 258, -301, 350, -400, 456, -513, 576, -640, 710, -781, 858, -936, 1020, -1105, 1196, -1288, 1386, -1485, 1590, -1696, 1808, -1921, 2040, -2160, 2286, -2413, 2546, -2680, 2820, -2961, 3108, -3256, 3410
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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 - 6*x)/((1 - x)*(1 + x)^3).
a(n) = ((14*n^2 + 4*n - 5)*(-1)^n + 5)/8.
a(n) = Sum_{k = 0..n} (-1)^k*A001106(k).
Lim_{n -> infinity} a(n + 1)/a(n) = -1.
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MATHEMATICA
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Table[((14 n^2 + 4 n - 5) (-1)^n + 5)/8, {n, 0, 44}]
CoefficientList[Series[(x - 6 x^2)/(x^4 + 2 x^3 - 2 x - 1), {x, 0, 50}], x] (* Vincenzo Librandi, Dec 21 2015 *)
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PROG
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(Magma) [(14*(-1)^n*n^2 + 4*(-1)^n*n - 5*(-1)^n + 5)/8: n in [0..50]]; // Vincenzo Librandi, Dec 21 2015
(PARI) x='x+O('x^100); concat(0, Vec(-x*(1-6*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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