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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A049681 a(n) = (L(2*n) - L(n))/2, where L=A000032 (the Lucas sequence). 2
0, 1, 2, 7, 20, 56, 152, 407, 1080, 2851, 7502, 19702, 51680, 135461, 354902, 929567, 2434320, 6374236, 16689752, 43697227, 114405500, 299525051, 784179002, 2053027082, 5374926720, 14071792681 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Create a triangle with T(n,1)=L(n-1) for L a Lucas number and the other side T(n,n)=L(2*(n-1)).  Interior elements are defined as T(r,c)=T(r-1,c-1)+T(r-1,c).  Half the sum of the terms in row(n)=a(n) for n=1,2,3...- J. M. Bergot, Dec 15 2012

LINKS

Robert Israel, Table of n, a(n) for n = 0..2380

Index entries for linear recurrences with constant coefficients, signature (4,-3,-2,1).

FORMULA

G.f.: -x*(1-2*x+2*x^2)/( (x^2+x-1)*(x^2-3*x+1) ). - R. J. Mathar, Dec 17 2012

a(n) = Lucas(n)*(Lucas(n) - 1)/2 - (-1)^n = binomial(Lucas(n), 2) - (-1)^n. - Vladimir Reshetnikov, Sep 27 2016

MAPLE

Lucas:= n -> combinat:-fibonacci(n+1)+combinat:-fibonacci(n-1):

seq((Lucas(2*n)-Lucas(n))/2, n=0..100); # Robert Israel, Sep 15 2016

MATHEMATICA

Table[(LucasL[2n] - LucasL[n])/2, {n, 0, 20}] (* Vladimir Reshetnikov, Sep 15 2016 *)

PROG

(PARI) x='x+O('x^30); concat([0], Vec(-x*(1-2*x+2*x^2)/( (x^2+x-1)*(x^2-3*x+1) ))) \\ G. C. Greubel, Dec 02 2017

(MAGMA) [(Lucas(2*n) - Lucas(n))/2: n in [0..30]]; // G. C. Greubel, Dec 02 2017

CROSSREFS

Cf. A094292.

Sequence in context: A018033 A000149 A080041 * A027120 A094982 A292400

Adjacent sequences:  A049678 A049679 A049680 * A049682 A049683 A049684

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

Corrected by Franklin T. Adams-Watters, Oct 25 2006

Corrected by T. D. Noe, Nov 01 2006

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 17 22:48 EDT 2018. Contains 316297 sequences. (Running on oeis4.)