A022130 Fibonacci sequence beginning 4,9.

4, 9, 13, 22, 35, 57, 92, 149, 241, 390, 631, 1021, 1652, 2673, 4325, 6998, 11323, 18321, 29644, 47965, 77609, 125574, 203183, 328757, 531940, 860697, 1392637, 2253334, 3645971, 5899305, 9545276, 15444581, 24989857, 40434438, 65424295, 105858733, 171283028

Offset

0,1

Comments

The associated Pisano series starts as in A001175, but differs for example for modulus 29 where it is 7, not 14. - R. J. Mathar, Nov 02 2011

The Pisano period also differs for modulus 58, where it is 21 instead of 42. Otherwise, the Pisano periods coincide with those of the Fibonacci numbers. - Klaus Purath, Jun 26 2022

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Tanya Khovanova, Recursive Sequences

H. Zhao and X. Li, On the Fibonacci numbers of trees, Fib. Quart., 44 (2006), 32-38.

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

Formula

a(n) = 4*Fibonacci(n+2) + Fibonacci(n).

G.f.: (4 + 5*x)/(1-x-x^2). - Philippe Deléham, Nov 19 2008

a(n)= Fibonacci(n-2) + Fibonacci(n+5). - Gary Detlefs, Mar 31 2012

Maple

a:= n-> (<<0|1>, <1|1>>^n.<<4, 9>>)[1, 1]:
seq(a(n), n=0..40);  # Alois P. Heinz, Feb 22 2017

Mathematica

a={}; b=4; c=9; AppendTo[a, b]; AppendTo[a, c]; Do[b=b+c; AppendTo[a, b]; c=b+c; AppendTo[a, c], {n, 1, 40, 1}]; a (* Vladimir Joseph Stephan Orlovsky, Jul 23 2008 *)
LinearRecurrence[{1, 1}, {4, 9}, 40] (* Harvey P. Dale, Dec 15 2011 *)

Prog

(PARI) a(n)=4*fibonacci(n-1)+9*fibonacci(n) \\ Charles R Greathouse IV, Jun 05 2011
(Magma) a0:=4; a1:=9; [GeneralizedFibonacciNumber(a0, a1, n): n in [0..35]]; // Vincenzo Librandi, Jan 25 2017

Crossrefs

Cf. A000032, A001175.

Sequence in context: A312986 A240692 A345743 * A042125 A041905 A098004

Adjacent sequences: A022127 A022128 A022129 * A022131 A022132 A022133

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved