A206609 Fibonacci sequence beginning 13, 9.

13, 9, 22, 31, 53, 84, 137, 221, 358, 579, 937, 1516, 2453, 3969, 6422, 10391, 16813, 27204, 44017, 71221, 115238, 186459, 301697, 488156, 789853, 1278009, 2067862, 3345871, 5413733, 8759604, 14173337, 22932941, 37106278, 60039219, 97145497, 157184716

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 Elmo R. Oliveira, Mar 30 2026: (Start)

G.f.: -(17*x - 4)/(x^2 + x - 1).

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

a(n) = 13*Fibonacci(n) - 4*Fibonacci(n-1). (End)

Maple

a:= n-> (<<0|1>, <1|1>>^n.<<-4, 13>>)[1, 1]:
seq(a(n), n=1..36);  # Alois P. Heinz, Mar 31 2026

Mathematica

LinearRecurrence[{1, 1}, {13, 9}, 80]

Prog

(Magma) I:=[13, 9]; [n le 2 select I[n] else Self(n-1)+Self(n-2): n in [1..40]]; // Vincenzo Librandi, Feb 16 2012

Crossrefs

Cf. A000032, A000045, A206607, A206608.

Sequence in context: A304137 A305043 A066552 * A392309 A281085 A072270

Adjacent sequences: A206606 A206607 A206608 * A206610 A206611 A206612

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Feb 10 2012

Status

approved