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A206423 Fibonacci sequence beginning 12, 7. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A093763 A002548 A305939 * A319406 A038333 A185259

Adjacent sequences:  A206420 A206421 A206422 * A206424 A206425 A206426

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Feb 07 2012

STATUS

approved

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Last modified August 10 07:57 EDT 2022. Contains 356036 sequences. (Running on oeis4.)