The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A094967 Right-hand neighbors of Fibonacci numbers in Stern's diatomic series. 8
 1, 1, 2, 2, 5, 5, 13, 13, 34, 34, 89, 89, 233, 233, 610, 610, 1597, 1597, 4181, 4181, 10946, 10946, 28657, 28657, 75025, 75025, 196418, 196418, 514229, 514229, 1346269, 1346269, 3524578, 3524578, 9227465, 9227465, 24157817, 24157817, 63245986, 63245986, 165580141, 165580141 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Fibonacci(2*n+1) repeated. a(n) is the right neighbor of Fibonacci(n+2) in A049456 and A002487 (starts 2,2,5,...). A000045(n+2) = A094966(n) + a(n). Diagonal sums of A109223. - Paul Barry, Jun 22 2005 The Fi2 sums, see A180662, of triangle A065941 equal the terms of this sequence. - Johannes W. Meijer, Aug 11 2011 a(n) is the last term of (n+1)-th row in Wythoff array A003603. -Reinhard Zumkeller, Jan 26 2012 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..2000 Jia Huang, Partially Palindromic Compositions, J. Int. Seq. (2023) Vol. 26, Art. 23.4.1. See pp. 4, 15. Index entries for linear recurrences with constant coefficients, signature (0,3,0,-1). FORMULA G.f.: (1+x-x^2-x^3)/(1-3*x^2+x^4). a(n) = Fibonacci(n)*(1-(-1)^n)/2 + Fibonacci(n+1)*(1+(-1)^n)/2. a(n) = Sum_{k=0..floor(n/2)} binomial(floor(n/2)+k, 2*k). - Paul Barry, Jun 22 2005 Starting (1, 2, 2, 5, 5, 13, 13, ...) = A133080 * A000045, where A000045 starts with "1". - Gary W. Adamson, Sep 08 2007 a(n) = Fibonacci(n+1)^(4*k+3) mod Fibonacci(n+2), for any k>-1, n>0. - Gary Detlefs, Nov 29 2010 MAPLE A094967 := proc(n) combinat[fibonacci](2*floor(n/2)+1) ; end proc: seq(A094967(n), n=0..37); MATHEMATICA LinearRecurrence[{0, 3, 0, -1}, {1, 1, 2, 2}, 40] (* Harvey P. Dale, Apr 05 2015 *) f[n_]:=If[OddQ@n, (Fibonacci[n]), Fibonacci[n+1]]; Array[f, 100, 0] (* Vincenzo Librandi, Nov 18 2018 *) Table[Fibonacci[n, 0]*Fibonacci[n] + LucasL[n, 0]*Fibonacci[n + 1]/2, {n, 0, 50}] (* G. C. Greubel, Nov 18 2018 *) PROG (Magma) [IsEven(n) select Fibonacci(n+1) else Fibonacci(n): n in [0..70]]; // Vincenzo Librandi, Nov 18 2018 (PARI) vector(50, n, n--; fibonacci(n)*(1-(-1)^n)/2 + fibonacci(n+1)*(1+(-1)^n)/2) \\ G. C. Greubel, Nov 18 2018 (Sage) [fibonacci(n)*(1-(-1)^n)/2 + fibonacci(n+1)*(1+(-1)^n)/2 for n in range(50)] # G. C. Greubel, Nov 18 2018 (GAP) List([0..50], n -> Fibonacci(n)*(1-(-1)^n)/2 + Fibonacci(n+1)*(1+(-1)^n)/2); # G. C. Greubel, Nov 18 2018 CROSSREFS Cf. A001519, A133080. Sequence in context: A338762 A364486 A178115 * A322111 A321395 A056505 Adjacent sequences: A094964 A094965 A094966 * A094968 A094969 A094970 KEYWORD easy,nonn AUTHOR Paul Barry, May 26 2004 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 May 20 23:09 EDT 2024. Contains 372720 sequences. (Running on oeis4.)