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A266085 Alternating sum of heptagonal numbers. 1
0, -1, 6, -12, 22, -33, 48, -64, 84, -105, 130, -156, 186, -217, 252, -288, 328, -369, 414, -460, 510, -561, 616, -672, 732, -793, 858, -924, 994, -1065, 1140, -1216, 1296, -1377, 1462, -1548, 1638, -1729, 1824, -1920, 2020, -2121, 2226, -2332, 2442, -2553 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

OEIS Wiki, Figurate numbers

Eric Weisstein's World of Mathematics, Heptagonal Number

Index entries for linear recurrences with constant coefficients, signature (-2,0,2,1).

FORMULA

G.f.: -x*(1 - 4*x)/((1 - x)*(1 + x)^3).

a(n) = ((10*n^2 + 4*n - 3)*(-1)^n + 3)/8.

a(n) = Sum_{k = 0..n} (-1)^k*A000566(k).

Lim_{n -> infinity} a(n + 1)/a(n) = -1.

a(n) = (-1)^n*A008728(5*n-5) for n>0. - Bruno Berselli, Dec 21 2015

MATHEMATICA

Table[((10 n^2 + 4 n - 3) (-1)^n + 3)/8, {n, 0, 50}]

CoefficientList[Series[(x - 4 x^2)/(x^4 + 2 x^3 - 2 x - 1), {x, 0, 50}], x] (* Vincenzo Librandi, Dec 21 2015 *)

PROG

(MAGMA) [((10*n^2+4*n-3)*(-1)^n+3)/8: n in [0..50]]; // Vincenzo Librandi, Dec 21 2015

(PARI) x='x+O('x^100); concat(0, Vec(-x*(1-4*x)/((1-x)*(1+x)^3))) \\ Altug Alkan, Dec 21 2015

CROSSREFS

Cf. A000566, A002413, A006578, A008728, A035608, A083392, A089594.

Sequence in context: A247212 A055458 A178733 * A144568 A222001 A078472

Adjacent sequences:  A266082 A266083 A266084 * A266086 A266087 A266088

KEYWORD

sign,easy

AUTHOR

Ilya Gutkovskiy, Dec 21 2015

STATUS

approved

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Last modified October 21 13:54 EDT 2018. Contains 316423 sequences. (Running on oeis4.)