A022114 Fibonacci sequence beginning 2 9.

2, 9, 11, 20, 31, 51, 82, 133, 215, 348, 563, 911, 1474, 2385, 3859, 6244, 10103, 16347, 26450, 42797, 69247, 112044, 181291, 293335, 474626, 767961, 1242587, 2010548, 3253135, 5263683, 8516818, 13780501, 22297319, 36077820, 58375139, 94452959, 152828098

Offset

0,1

Links

Ivan Panchenko, Table of n, a(n) for n = 0..1000

Bruce M. Boman, How Does Multicellular Life Happen? Modeling Fibonacci Patterns in Biological Tissues Unveils Underlying Mechanisms, Fibonacci Quarterly (September 2025). See p. 5 (Table 1), Fig. 6, Table 3, pp. 10, 13.

Tanya Khovanova, Recursive Sequences.

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

Formula

G.f.: (2+7*x)/(1-x-x^2). - Wesley Ivan Hurt, Jun 15 2014

a(n) = 10*F(n) + F(n-3). - J. M. Bergot, Jul 17 2017

a(n) = Fibonacci(n+5) - Lucas(n-2). - Greg Dresden and Christina Savory, Mar 01 2022

Mathematica

LinearRecurrence[{1, 1}, {2, 9}, 40] (* Harvey P. Dale, Jul 16 2012 *)
CoefficientList[Series[(2 + 7 x)/(1 - x - x^2), {x, 0, 40}], x] (* Wesley Ivan Hurt, Jun 15 2014 *)

Prog

(Magma) a0:=2; a1:=9; [GeneralizedFibonacciNumber(a0, a1, n): n in [0..40]]; // Bruno Berselli, Feb 12 2013

Crossrefs

Cf. A000032, A000045.

Sequence in context: A049343 A395113 A131140 * A041099 A041581 A042463

Adjacent sequences: A022111 A022112 A022113 * A022115 A022116 A022117

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 14 1998

Status

approved