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A049667 a(n) = F(7*n)/13, where F = A000045 (the Fibonacci sequence). 9
0, 1, 29, 842, 24447, 709805, 20608792, 598364773, 17373187209, 504420793834, 14645576208395, 425226130837289, 12346203370489776, 358465123875040793, 10407834795746672773, 302185674200528551210, 8773792386611074657863 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..650

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (29, 1).

FORMULA

G.f.: x/(1 - 29*x - x^2).

a(n) = A134498(n)/13.

a(n) = F(n, 29), the n-th Fibonacci polynomial evaluated at x=29. - T. D. Noe, Jan 19 2006

a(n) = 29*a(n-1) + a(n-2), n>1; a(0)=0, a(1)=1. - Philippe Deléham, Nov 22 2008

a(n) = ((-1)^n*7*F(n) + 14*5*F(n)^3 + (-1)^n*7*5^2*F(n)^5 + 5^3*F(n)^7)/13, n >= 0. See the general D. Jennings formula given in comment on triangle A111125, where also the reference is given. Here the fourth row (k=3) applies. - Wolfdieter Lang, Sep 01 2012

G.f.: G(0)*x/(2-29*x), where G(k)= 1 + 1/(1 - (x*(845*k-841))/((x*(845*k+4)) - 58/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 15 2013

MAPLE

a:= n-> (<<0|1>, <1|29>>^n)[1, 2]:

seq(a(n), n=0..20);  # Alois P. Heinz, Sep 20 2017

MATHEMATICA

Fibonacci[(7*Range[0, 20])]/13 (* or *) LinearRecurrence[{29, 1}, {0, 1}, 20] (* Harvey P. Dale, Sep 17 2017 *)

PROG

(Mupad) numlib::fibonacci(7*n)/13 $ n = 0..25; # Zerinvary Lajos, May 09 2008

(Sage) [fibonacci(7*n)/13 for n in xrange(0, 17)] # Zerinvary Lajos, May 15 2009

(PARI) a(n)=fibonacci(7*n)/13 \\ Charles R Greathouse IV, Oct 07 2016

(MAGMA) [Fibonacci(7*n)/13: n in [0..30]]; // G. C. Greubel, Dec 02 2017

CROSSREFS

A column of array A028412.

Cf. A134498.

Sequence in context: A009973 A278475 A057687 * A042626 A157877 A158665

Adjacent sequences:  A049664 A049665 A049666 * A049668 A049669 A049670

KEYWORD

nonn,easy,changed

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified December 15 14:37 EST 2017. Contains 296039 sequences.