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!)
 A033891 a(n) = Fibonacci(4*n+3). 16
 2, 13, 89, 610, 4181, 28657, 196418, 1346269, 9227465, 63245986, 433494437, 2971215073, 20365011074, 139583862445, 956722026041, 6557470319842, 44945570212853, 308061521170129, 2111485077978050 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (7,-1). FORMULA a(n) = 7*a(n-1)-a(n-2). - Floor van Lamoen, Dec 10 2001 a(n) = (7/2-(3/2)*sqrt(5))^n-(2/5)*(7/2-(3/2)*sqrt(5))^n*sqrt(5)+(2/5)*sqrt(5)*(7/2+(3/2) *sqrt(5))^n+(7/2+(3/2)*sqrt(5))^n, with n>=0. - Paolo P. Lava, Jun 25 2008 G.f.: (2-x)/(1-7*x+x^2). - Philippe Deléham, Nov 17 2008 a(n) = A167816(4*n+3). - Reinhard Zumkeller, Nov 13 2009 a(n) = Fibonacci(2*n+2)^2 + Fibonacci(2*n+1)^2. - Gary Detlefs, Oct 12 2011 a(n) = 2*A004187(n+1)-A004187(n). - R. J. Mathar, Nov 26 2011 a(n) = A004187(n+1) + A049685(n). - Yuriy Sibirmovsky, Sep 15 2016 MATHEMATICA Table[Fibonacci[4*n+3], {n, 0, 14}] (* Vladimir Joseph Stephan Orlovsky, Jul 21 2008 *) LinearRecurrence[{7, -1}, {2, 13}, 31] (* or *) CoefficientList[Series[ (2-x)/(1-7x+x^2), {x, 0, 30}], x] (* Harvey P. Dale, May 03 2011 *) PROG (MAGMA) [Fibonacci(4*n +3): n in [0..100]]; // Vincenzo Librandi, Apr 17 2011 (PARI) a(n)=fibonacci(4*n+3) \\ Charles R Greathouse IV, Sep 24 2015 CROSSREFS Cf. A000045, A004187, A049685, A167816. Sequence in context: A092849 A106938 A106937 * A172968 A126035 A074617 Adjacent sequences:  A033888 A033889 A033890 * A033892 A033893 A033894 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.