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A087452 G.f.: (2-x)/((1+3x)(1-4x)); e.g.f.: exp(4x)+exp(-3x); a(n)=4^n+(-3)^n. 1

%I

%S 2,1,25,37,337,781,4825,14197,72097,242461,1107625,4017157,17308657,

%T 65514541,273218425,1059392917,4338014017,17050729021,69106897225,

%U 273715645477,1102998412177,4387586157901,17623567104025,70274600998837,281757406247137

%N G.f.: (2-x)/((1+3x)(1-4x)); e.g.f.: exp(4x)+exp(-3x); a(n)=4^n+(-3)^n.

%C Generalized Lucas-Jacobsthal numbers.

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (1,12).

%F The sequence 1, 25, 37, ... is 4*4^n-3*(-3)^n.

%F a(0)=2, a(1)=1, a(n)=a(n-1)+12*a(n-2) for n>1. [From _Philippe Deléham_, Sep 19 2009]

%F a(n) = 2*A053404(n) - A053404(n-1), n>0. - _Ralf Stephan_, Jul 21 2013

%t CoefficientList[Series[(2 - z)/((1 + 3 z) (1 - 4 z)), {z, 0, 200}], z] (* _Vladimir Joseph Stephan Orlovsky_, Jun 11 2011 *)

%o (PARI) polsym(x^2-x-12,50) \\ _Charles R Greathouse IV_, Jun 11 2011

%Y Cf. A014551, A087451.

%K easy,nonn

%O 0,1

%A _Paul Barry_, Sep 06 2003

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Last modified December 9 04:50 EST 2016. Contains 278960 sequences.