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A232015 Expansion of (1-2*x)/((1+2*x)*(1-3*x)). 2

%I

%S 1,-1,5,-1,29,23,197,335,1517,3527,12629,33791,109565,312311,969701,

%T 2843567,8661773,25723175,77693813,232032863,698195741,2090392919,

%U 6279567365,18821924879,56499329069,169430878343,508426852757,1525012122815,4575573239357

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

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,6).

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

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

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

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

%F From _Bruno Berselli_, Nov 18 2013: (Start)

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

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

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

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

%t Table[(3^n + 4 (-2)^n)/5, {n, 0, 30}] (* _Bruno Berselli_, Nov 18 2013 *)

%t 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 *)

%o (PARI) Vec((1-2*x)/((1+2*x)*(1-3*x))+O(x^20)) \\ _Edward Jiang_, Sep 06 2014

%Y Cf. A078008, A108561.

%K sign,easy

%O 0,3

%A _Philippe Deléham_, Nov 17 2013

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Last modified July 24 03:30 EDT 2019. Contains 325290 sequences. (Running on oeis4.)