|
%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/Rea#recLCC">Index to sequences with linear recurrences with constant coefficients</a>, signature (1,12).
%F The sequence 1, 25, 35, ... 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 DELEHAM_, Sep 19 2009]
%t CoefficientList[Series[(2 - z)/((1 + 3 z) (1 - 4 z)), {z, 0, 200}], z] (* From 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,changed
%O 0,1
%A _Paul Barry_, Sep 06 2003
|
