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

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A146005 a(n) = n*Lucas(n). 2
0, 1, 6, 12, 28, 55, 108, 203, 376, 684, 1230, 2189, 3864, 6773, 11802, 20460, 35312, 60707, 104004, 177631, 302540, 513996, 871266, 1473817, 2488368, 4194025, 7057518, 11858508, 19898116, 33345679, 55814940, 93320819, 155867104 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

FORMULA

a(n) = n*A000032(n).

G.f.: x(1+4x-x^2)/(1-x-x^2)^2.

a(n) = 2*a(n-1)+a(n-2)-2*a(n-3)-a(n-4).

a(n) = A000045(n)-5*A000045(n+1)+5*A010049(n+1).

a(n) = A045925(n)+2*A099920(n-1).

E.g.f.: x*exp(x/2)*(cosh(sqrt(5)*x/2) + sqrt(5)*sinh(sqrt(5)*x/2)). - G. C. Greubel, Jan 30 2016

MATHEMATICA

Table[LucasL[n, 1]*n, {n, 0, 36}] (* Zerinvary Lajos, Jul 09 2009 *)

CoefficientList[Series[x * (1 + 4*x - x^2)/(1 - x - x^2)^2, {x, 0, 40}], x] (* Vincenzo Librandi, Dec 13 2012 *)

LinearRecurrence[{2, 1, -2, -1}, {0, 1, 6, 12}, 40] (* Harvey P. Dale, Apr 03 2013 *)

PROG

(MAGMA) I:=[0, 1, 6, 12]; [n le 4 select I[n] else 2*Self(n-1) + Self(n-2) - 2*Self(n-3) - Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 13 2012

CROSSREFS

Sequence in context: A057341 A068412 A183026 * A223346 A109510 A034715

Adjacent sequences:  A146002 A146003 A146004 * A146006 A146007 A146008

KEYWORD

easy,nonn

AUTHOR

R. J. Mathar, Oct 26 2008

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 December 11 14:03 EST 2017. Contains 295884 sequences.