A232015 - OEIS

A232015

Expansion of (1-2*x)/((1+2*x)*(1-3*x)).

1, -1, 5, -1, 29, 23, 197, 335, 1517, 3527, 12629, 33791, 109565, 312311, 969701, 2843567, 8661773, 25723175, 77693813, 232032863, 698195741, 2090392919, 6279567365, 18821924879, 56499329069, 169430878343, 508426852757, 1525012122815, 4575573239357

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..28.

Index entries for linear recurrences with constant coefficients, signature (1,6).

FORMULA

G.f.: (1 - 2*x) / (1 - x - 6*x^2).

a(n) = a(n-1) + 6*a(n-2) for n>1, a(0)=1, a(1)=-1.

a(n) = sum_{k=0..n} A108561(n,k)*2^k.

a(n) = A102901(n) - A015441(n).

From Bruno Berselli, Nov 18 2013: (Start)

a(n) = (3^n + 4*(-2)^n)/5.

a(n+1) + a(n) = 4*A015441(n).

a(n+1) - a(n) = -2*(-1)^n*A165405(n).

Sum(a(i), i=0..n) = A091001(n+1). (End)

MATHEMATICA

Table[(3^n + 4 (-2)^n)/5, {n, 0, 30}] (* Bruno Berselli, Nov 18 2013 *)

CoefficientList[Series[(1-2x)/((1+2x)(1-3x)), {x, 0, 40}], x] (* or *) LinearRecurrence[ {1, 6}, {1, -1}, 30] (* Harvey P. Dale, Apr 20 2017 *)

PROG

(PARI) Vec((1-2*x)/((1+2*x)*(1-3*x))+O(x^20)) \\ Edward Jiang, Sep 06 2014

CROSSREFS

Cf. A078008, A108561.

Sequence in context: A146414 A146374 A188647 * A214882 A144890 A144891

Adjacent sequences: A232012 A232013 A232014 * A232016 A232017 A232018

KEYWORD

sign,easy

AUTHOR

Philippe Deléham, Nov 17 2013

STATUS

approved