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A022116 Fibonacci sequence beginning 2, 13. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A089019 A015905 A179164 * A041201 A042155 A295336

Adjacent sequences:  A022113 A022114 A022115 * A022117 A022118 A022119

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Jun 14 1998

STATUS

approved

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Last modified July 8 20:50 EDT 2020. Contains 335535 sequences. (Running on oeis4.)