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

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

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)

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 *)

Prog

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

Crossrefs

Cf. A000045.

Sequence in context: A089487 A166521 A187866 * A250032 A305447 A060954

Adjacent sequences: A206416 A206417 A206418 * A206420 A206421 A206422

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Feb 07 2012

Status

approved