A221173 a(0)=-3, a(1)=4; thereafter a(n) = 2*a(n-1) + a(n-2).

-3, 4, 5, 14, 33, 80, 193, 466, 1125, 2716, 6557, 15830, 38217, 92264, 222745, 537754, 1298253, 3134260, 7566773, 18267806, 44102385, 106472576, 257047537, 620567650, 1498182837, 3616933324, 8732049485, 21081032294, 50894114073, 122869260440, 296632634953

Offset: 0

Author

N. J. A. Sloane, Jan 04 2013

Keywords

• sign
• easy

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
• José L. Ramírez, Gustavo N. Rubiano, and Rodrigo de Castro, A Generalization of the Fibonacci Word Fractal and the Fibonacci Snowflake, arXiv preprint arXiv:1212.1368 [cs.DM], 2012-2014.
• Index entries for linear recurrences with constant coefficients, signature (2,1).

Crossrefs

Cf. A000129, A078343, A221172, A221174, A221175.

Programs

Haskell

a221173 n = a221173_list !! n
a221173_list = -3 : 4 : zipWith (+)
                        (map (* 2) $ tail a221173_list) a221173_list
-- Reinhard Zumkeller, Jan 04 2013

Mathematica

LinearRecurrence[{2,1},{-3,4},50] (* Harvey P. Dale, Apr 09 2022 *)

PARI

Vec(-(10*x-3)/(x^2+2*x-1) + O(x^100)) \\ Colin Barker, Jul 10 2015

Formula

a(n) = 10*A000129(n)-3*A000129(n+1). - R. J. Mathar, Jan 14 2013

G.f.: -(10*x-3) / (x^2+2*x-1). - Colin Barker, Jul 10 2015