A060405 Sum of n-th Lucas number (A000032(n)) and n-th Pell number (A000129(n)).

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

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

From Colin Barker, Jun 22 2012: (Start)

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)). (End)

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

Example

a(6) = Lucas(6) + Pell(6) = 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