A022116 Fibonacci sequence beginning 2, 13.

2, 13, 15, 28, 43, 71, 114, 185, 299, 484, 783, 1267, 2050, 3317, 5367, 8684, 14051, 22735, 36786, 59521, 96307, 155828, 252135, 407963, 660098, 1068061, 1728159, 2796220, 4524379, 7320599, 11844978, 19165577, 31010555, 50176132, 81186687, 131362819

Offset

0,1

Links

Ivan Panchenko, Table of n, a(n) for n = 0..1000

Tanya Khovanova, Recursive Sequences

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

Formula

G.f.: (2 + 11*x)/(1-x-x^2). - Philippe Deléham, Nov 19 2008

a(n) = 4*Fibonacci(n+2) + 3*Fibonacci(n+3) - 4*Lucas(n). - Lechoslaw Ratajczak, Feb 10 2020

E.g.f.: (2/5)*exp(x/2)*(5*cosh(sqrt(5)*x/2) + 12*sqrt(5)*sinh(sqrt(5)*x/2)). - Stefano Spezia, Feb 11 2020

a(n) = 2*Fibonacci(n+2) + 9*Fibonacci(n). - G. C. Greubel, Feb 12 2020

Maple

seq( 2*fibonacci(n+2) +9*fibonacci(n), n=0..40); # G. C. Greubel, Feb 12 2020

Mathematica

CoefficientList[Series[(2+11x)/(1-x-x^2), {x, 0, 40}], x] (* Wesley Ivan Hurt, Jun 15 2014 *)
LinearRecurrence[{1, 1}, {2, 13}, 50] (* Harvey P. Dale, Jun 20 2017 *)

Prog

(Magma) a:=[2, 13]; [n le 2 select a[n] else Self(n-1)+Self(n-2): n in [1..36]]; // Marius A. Burtea, Feb 11 2020
(Magma) R<x>:=PowerSeriesRing(Integers(), 36); Coefficients(R!( (2+11*x)/(1-x-x^2))); // Marius A. Burtea, Feb 11 2020
(PARI) vector(41, n, my(m=n-1, f=fibonacci); 2*f(m+2) + 9*f(m) ) \\ G. C. Greubel, Feb 12 2020
(Sage) [2*fibonacci(n+2) + 9*fibonacci(n) for n in (0..40)] # G. C. Greubel, Feb 12 2020

Crossrefs

Cf. A000032, A000045.

Sequence in context: A015905 A179164 A356102 * A041201 A042155 A295336

Adjacent sequences: A022113 A022114 A022115 * A022117 A022118 A022119

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 14 1998

Status

approved