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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A060405 Sum of Lucas (A000032) and Pell (A000129) numbers. 2
2, 2, 5, 9, 19, 40, 88, 198, 455, 1061, 2501, 5940, 14182, 33982, 81625, 196389, 473039, 1140260, 2749988, 6634458, 16009555, 38638441, 93261961, 225122760, 543443402, 1311905882, 3167087405, 7645809249, 18458266699, 44561632000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (3,0,-3,-1).

FORMULA

a(n) = 3*a(n-1)-3*a(n-3)-a(n-4). G.f.: (2-4*x-x^2)/((1-x-x^2)*(1-2*x-x^2)). [Colin Barker, Jun 22 2012]

a(n) = A000129(n) + A000032(n). [Jonathan Vos Post, Sep 02 2013]

EXAMPLE

18+70 = 88.

MAPLE

gfpell := x/(1-2*x-x^2): gfluc := (2-x)/(1-x-x^2): s := series(gfpell+gfluc, x, 100): for i from 0 to 60 do printf(`%d, `, coeff(s, x, i)) od:

MATHEMATICA

LinearRecurrence[{3, 0, -3, -1}, {2, 2, 5, 9}, 30] (* Harvey P. Dale, Jun 05 2017 *)

PROG

(MAGMA) I:=[2, 2, 5, 9]; [n le 4 select I[n] else 3*Self(n-1)-3*Self(n-3)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Juan 07 2017

CROSSREFS

Cf. A000032, A000129, A001932, A226638 Product of Pell and Lucas numbers.

Sequence in context: A302483 A052969 A002990 * A326493 A003228 A184713

Adjacent sequences:  A060402 A060403 A060404 * A060406 A060407 A060408

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Apr 05 2001

EXTENSIONS

More terms from James A. Sellers, Apr 06 2001

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 15 15:01 EST 2019. Contains 329999 sequences. (Running on oeis4.)