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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 * A003228 A184713 A110182

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

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Last modified August 20 08:27 EDT 2019. Contains 326143 sequences. (Running on oeis4.)