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A232599 Alternating sum of cubes, i.e., sum[k=0..n] k^p*q^k for p=3,q=-1. 12
0, -1, 7, -20, 44, -81, 135, -208, 304, -425, 575, -756, 972, -1225, 1519, -1856, 2240, -2673, 3159, -3700, 4300, -4961, 5687, -6480, 7344, -8281, 9295, -10388, 11564, -12825, 14175, -15616, 17152, -18785, 20519 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Stanislav Sykora, Table of n, a(n) for n = 0..1000

S. Sykora, Finite and Infinite Sums of the Power Series (k^p)(x^k), DOI 10.3247/SL1Math06.002, Section V.

Index entries for linear recurrences with constant coefficients, signature (-3,-2,2,3,1).

FORMULA

a(n)=((-1)^n*(4*n^3+6*n^2-1)+1)/8.

G.f.: x*(1-4*x+x^2) / ( (x-1)*(1+x)^4 ). - R. J. Mathar, Nov 23 2014

EXAMPLE

a(3) = 0^3 - 1^3 + 2^3 - 3^3 = -20.

MATHEMATICA

Accumulate[Times@@@Partition[Riffle[Range[0, 40]^3, {1, -1}, {2, -1, 2}], 2]] (* Harvey P. Dale, Jul 22 2016 *)

PROG

(PARI) S3M1(n)=((-1)^n*(4*n^3+6*n^2-1)+1)/8;

v = vector(10001); for(k=1, #v, v[k]=S3M1(k-1))

CROSSREFS

Cf. A000578 (cubes), A011934 (absolute values), A059841 (p=0,q=-1), A130472 (p=1,q=-1), A089594 (p=2,q=-1), A00079 (p=0,q=2), A036799 (p=1,q=2), A036800 (p=2,q=2), A036827 (p=3,q=2), A077925 (p=0,q=-2), A232600 (p=1,q=-2), A232601 (p=2,q=-2), A232602 (p=3,q=-2), A232603 (p=2,q=-1/2), A232604 (p=3,q=-1/2).

Sequence in context: A162024 A143058 A175428 * A011934 A159222 A100206

Adjacent sequences:  A232596 A232597 A232598 * A232600 A232601 A232602

KEYWORD

sign,easy

AUTHOR

Stanislav Sykora, Nov 26 2013

STATUS

approved

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Last modified May 22 16:19 EDT 2017. Contains 286882 sequences.