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A049669 a(n)=F(9n)/34, where F=A000045 (the Fibonacci sequence). 3
0, 1, 76, 5777, 439128, 33379505, 2537281508, 192866774113, 14660412114096, 1114384187445409, 84707858657965180, 6438911642192799089, 489441992665310695944, 37204030354205805690833 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

S. Falcon, Generalized Fibonacci Sequences Generated from a k-Fibonacci Sequence, Journal of Mathematics Research Vol. 4, No. 2; April 2012; http://journal.ccsenet.org/index.php/jmr/article/viewFile/14516/10822. - From N. J. A. Sloane, Sep 22 2012

LINKS

Table of n, a(n) for n=0..13.

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (76, 1).

FORMULA

G.f. x/(1-76*x-x^2), 76=L(9)=A000032(9) (Lucas).

a(n)=76*a(n-1)+a(n-2), n>1 ; a(0)=0, a(1)=1 . [From Philippe Deléham, Nov 23 2008]

a(n) = (9*F(n) + (-1)^n*30*5*F(n)^3 + 27*5^2*F(n)^5 + (-1)^n*9*5^3*F(n)^7 + 5^4*F(n)^9)/34, n >= 0. See the general D. Jennings formula given in a comment on the triangle A111125, where also the reference is given. Here the fifth row (k=4) applies. - Wolfdieter Lang, Sep 01 2012

MAPLE

with (combinat):seq(fibonacci(3*n, 4)/17, n=0..13); - Zerinvary Lajos, Apr 20 2008

MATHEMATICA

Fibonacci[9Range[0, 20]]/34 (* or *) LinearRecurrence[{76, 1}, {0, 1}, 20] (* Harvey P. Dale, Jan 20 2013 *)

PROG

(Mupad) numlib::fibonacci(9*n)/34 $ n = 0..25; - Zerinvary Lajos, May 09 2008

CROSSREFS

A column of array A028412.

Sequence in context: A234176 A116264 A004299 * A198476 A234778 A139671

Adjacent sequences:  A049666 A049667 A049668 * A049670 A049671 A049672

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

More terms from James A. Sellers, Jan 20 2000

STATUS

approved

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Last modified April 28 05:37 EDT 2017. Contains 285557 sequences.