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A022130 Fibonacci sequence beginning 4,9. 7
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 (list; graph; refs; listen; history; text; internal format)
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

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.

Sequence in context: A141224 A064423 A240692 * A042125 A041905 A098004

Adjacent sequences:  A022127 A022128 A022129 * A022131 A022132 A022133

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified March 29 17:18 EDT 2017. Contains 284273 sequences.