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A077903 Expansion of (1-x)^(-1)/(1+x-x^2+2*x^3). 0
1, 0, 2, -3, 6, -12, 25, -48, 98, -195, 390, -780, 1561, -3120, 6242, -12483, 24966, -49932, 99865, -199728, 399458, -798915, 1597830, -3195660, 6391321, -12782640, 25565282, -51130563, 102261126, -204522252, 409044505, -818089008, 1636178018, -3272356035, 6544712070 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Convolution of A010892(n) and (-1)^n*A001045(n+1). The positive sequence has g.f. 1/((1-x-2x^2)(1+x+x^2)). This is the convolution of A001045(n+1) and A049347(n). - Paul Barry, May 19 2004

LINKS

Table of n, a(n) for n=0..34.

Index entries for linear recurrences with constant coefficients, signature (0,2,-3,2)

FORMULA

G.f. : 1/((1+x-2x^2)(1-x+x^2)); a(n)=sum{k=0..n, (2*(-2)^k/3+1/3)2sin(pi*(n-k)/3+pi/3)/sqrt(3)}; a(n)=2^(n+3)cos(pi*n)/21+8sqrt(3)cos(pi*n/3+pi/6)/63+4sqrt(3)sin(pi*n/3+pi/3)/63 +2sqrt(3)sin(pi*n/3)/9+1/3; - Paul Barry, May 19 2004

a(n) = 1/3 +(-1)^n*2^(n+3)/21 - A117373(n+1)/7. - R. J. Mathar, Sep 27 2012

MATHEMATICA

CoefficientList[Series[(1-x)^(-1)/(1+x-x^2+2x^3), {x, 0, 40}], x] (* or *) LinearRecurrence[{0, 2, -3, 2}, {1, 0, 2, -3}, 40] (* Harvey P. Dale, Apr 25 2016 *)

CROSSREFS

Sequence in context: A045761 A187741 A216632 * A038086 A032305 A032218

Adjacent sequences:  A077900 A077901 A077902 * A077904 A077905 A077906

KEYWORD

sign

AUTHOR

N. J. A. Sloane, Nov 17 2002

STATUS

approved

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Last modified December 9 10:32 EST 2016. Contains 278971 sequences.