A206419 Fibonacci sequence beginning 11, 7.

11, 7, 18, 25, 43, 68, 111, 179, 290, 469, 759, 1228, 1987, 3215, 5202, 8417, 13619, 22036, 35655, 57691, 93346, 151037, 244383, 395420, 639803, 1035223, 1675026, 2710249, 4385275, 7095524, 11480799, 18576323, 30057122, 48633445, 78690567, 127324012

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Feb 07 2012

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1, 1).

Crossrefs

Cf. A000045.

Programs

Magma

I:=[11, 7]; [n le 2 select I[n] else Self(n-1)+Self(n-2): n in [1..50]]; // Vincenzo Librandi, Feb 18 2012

Mathematica

LinearRecurrence[{1, 1}, {11, 7}, 60]
CoefficientList[Series[x (11-4x)/(1-x-x^2),{x,0,40}],x] (* Harvey P. Dale, Jun 24 2021 *)

PARI

Vec((11 - 4*x)/(1 - x - x^2) + O(x^30)) \\ Andrew Howroyd, Aug 28 2018

Formula

From Andrew Howroyd, Aug 28 2018: (Start)

a(n) = a(n-1) + a(n-2) for n > 2.

a(n) = 11*Fibonacci(n) - 4*Fibonacci(n-1).

G.f.: x*(11 - 4*x)/(1 - x - x^2).

(End)