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A232600 Sum( k=0..n, k^p*q^k ), where p=1, q=-2. 10
0, -2, 6, -18, 46, -114, 270, -626, 1422, -3186, 7054, -15474, 33678, -72818, 156558, -334962, 713614, -1514610, 3203982, -6757490, 14214030, -29826162, 62448526, -130489458, 272163726, -566697074, 1178133390, -2445745266, 5070447502, -10498808946, 21713445774 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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 (-3,0,4).

FORMULA

a(n) = -( (3*n+1)*(-2)^(n+1) + 2 )/9.

abs(a(n)) = 2*A045883(n) = A140960(n).

G.f.: -2*x / ((1 + x)*(1 + 2*x)^2). [Bruno Berselli, Nov 28 2013]

a(n) = -3*a(n-1) +4*a(n-3). [Bruno Berselli, Nov 28 2013]

EXAMPLE

a(3) = 0^1*2^0 - 1^1*2^1 + 2^1*2^2 - 3^1*2^3 = -18.

MATHEMATICA

Table[-((3 n + 1) (-2)^(n + 1) + 2)/9, {n, 0, 30}] (* Bruno Berselli, Nov 28 2013 *)

PROG

(PARI) a(n)=-((3*n+1)*(-2)^(n+1)+2)/9;

CROSSREFS

Cf. A045883, A140960 (absolute values), A059841 (p=0, q=-1), A130472 (p=1 ,q=-1), A089594 (p=2, q=-1), A232599 (p=3, q=-1), A126646 (p=0, q=2), A036799 (p=1, q=2), A036800 (p=q=2), A036827 (p=3, q=2), A077925 (p=0, 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: A120414 A251685 A054136 * A140960 A072827 A248169

Adjacent sequences:  A232597 A232598 A232599 * A232601 A232602 A232603

KEYWORD

sign,easy

AUTHOR

Stanislav Sykora, Nov 27 2013

STATUS

approved

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Last modified August 20 03:34 EDT 2017. Contains 290823 sequences.