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A022130 Fibonacci sequence beginning 4,9. 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 (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
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
Tanya Khovanova, Recursive Sequences
H. Zhao and X. Li, On the Fibonacci numbers of trees, Fib. Quart., 44 (2006), 32-38.
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
Sequence in context: A312986 A240692 A345743 * A042125 A041905 A098004
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified July 13 00:23 EDT 2024. Contains 374259 sequences. (Running on oeis4.)