login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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/Rea#recLCC">Index to sequences with 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified December 22 02:57 EST 2014. Contains 252326 sequences.