This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A049667 a(n) = F(7n)/13, where F = A000045 (the Fibonacci sequence). 8
 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 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 a=0; lst={a}; s=0; Do[a=s-(a-1); AppendTo[lst, a]; s+=a*29, {n, 3*4!}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 27 2009 *) 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 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 AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.