The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A033192 a(n) = binomial(Fibonacci(n) + 1, 2). 9
 0, 1, 1, 3, 6, 15, 36, 91, 231, 595, 1540, 4005, 10440, 27261, 71253, 186355, 487578, 1276003, 3339820, 8742471, 22885995, 59912931, 156848616, 410626153, 1075018896, 2814412825, 7368190921, 19290113571, 50502074766, 132215989335, 346145696820, 906220783315 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS a(n) is the sum of n-th row in Wythoff array A003603. [Reinhard Zumkeller, Jan 26 2012] A subsequence of the triangular numbers A000217. In fact, binomial(F(n)+1,2) = A000217(F(n)). - M. F. Hasler, Jan 27 2012 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..2394 James P. Jones, Péter Kiss, Representation of integers as terms of a linear recurrence with maximal index, Acta Academiae Paedagogicae Agriensis, Sectio Mathematicae, 25. (1998) pp. 21-37. See Theorem 3.7 p. 33. Index entries for linear recurrences with constant coefficients, signature (3,1,-5,-1,1). FORMULA G.f.: x(x^3-x^2-2x+1)/[(1+x)(1-3x+x^2)(1-x-x^2)]. a(n) = ((Fibonacci(n)+Fibonacci(n)^2)/2). - Gary Detlefs Dec 24 2010 Equals A000217 o A000045. - M. F. Hasler, Jan 27 2012 a(n) = A032441(n) - 1. - Filip Zaludek, Oct 30 2016 MAPLE a:= n-> (f-> f*(f+1)/2)((<<0|1>, <1|1>>^n)[1, 2]): seq(a(n), n=0..35); # Alois P. Heinz, Sep 06 2008 MATHEMATICA Table[Binomial[Fibonacci[n] + 1, 2], {n, 0, 50}] (* Alonso del Arte, Jan 26 2012 *) LinearRecurrence[{3, 1, -5, -1, 1}, {0, 1, 1, 3, 6}, 40] (* Harvey P. Dale, Apr 04 2020 *) PROG (PARI) a(n)=binomial(fibonacci(n)+1, 2) \\ Charles R Greathouse IV, Jan 26 2012 CROSSREFS Cf. A000045, A000217, A033191, A081667. Sequence in context: A291013 A017924 A052827 * A174297 A005043 A099323 Adjacent sequences: A033189 A033190 A033191 * A033193 A033194 A033195 KEYWORD nonn,easy AUTHOR Simon P. Norton (simon(AT)dpmms.cam.ac.uk) STATUS approved

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

Last modified December 5 05:50 EST 2022. Contains 358578 sequences. (Running on oeis4.)