A206423 Fibonacci sequence beginning 12, 7.

12, 7, 19, 26, 45, 71, 116, 187, 303, 490, 793, 1283, 2076, 3359, 5435, 8794, 14229, 23023, 37252, 60275, 97527, 157802, 255329, 413131, 668460, 1081591, 1750051, 2831642, 4581693, 7413335, 11995028, 19408363, 31403391, 50811754, 82215145, 133026899, 215242044

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) = 12*Fibonacci(n) - 5*Fibonacci(n-1).

G.f.: x*(12 - 5*x)/(1 - x - x^2).

(End)

Mathematica

LinearRecurrence[{1, 1}, {12, 7}, 60]

Prog

(Magma) I:=[12, 7]; [n le 2 select I[n] else Self(n-1)+Self(n-2): n in [1..40]]; \\ Vincenzo Librandi, Feb 17 2012
(PARI) Vec((12 - 5*x)/(1 - x - x^2) + O(x^30)) \\ Andrew Howroyd, Aug 28 2018
(Python)
alst, terms = [12, 7], 37
[alst.append(alst[n-1] + alst[n-2]) for n in range(2, terms)]
print(alst) # Michael S. Branicky, Dec 07 2021

Crossrefs

Cf. A000045.

Sequence in context: A359632 A364135 A305939 * A319406 A038333 A185259

Adjacent sequences: A206420 A206421 A206422 * A206424 A206425 A206426

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Feb 07 2012

Status

approved