Re: In einem Link das gefunden (schon bekannt ;-)?): Mit Literatur für Fibo-Fraks

verfasst von AU, 21.05.2001, 16:49

Hallo"Dottore"
n Sie den Fehler auf

Seite"drei" schon entdeckt?!

Nur sol als kleiner allgemeiner Hinweis!


PFG

AU
habe

>ID Number: A000045 (Formerly M0692 and N0256)
>Sequence: 0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,
> 4181,6765,10946,17711,28657,46368,75025,121393,196418,
> 317811,514229,832040,1346269,2178309,3524578,5702887,
> 9227465,14930352,24157817,39088169
>Name: Fibonacci numbers: F(n) = F(n-1) + F(n-2), F(0) = 0, F(1) = 1, F(2) = 1,...
>Comments: F(n+1) = number of binary sequences of length n that have no consecutive
> 0's.
> F(n+2) = number of subsets of {1,2,...,n} that contain no consecutive
> integers.
> F(n+1) = number of tilings of a 2xn rectangle by 2x1 dominos.
> Positive terms are the solutions to z = 2xy^4 + (x^2)y^3 - 2(x^3)y^2 - y^5
> - (x^4)y + 2y for x,y >= 0 (Ribenboim, page 193). When x=F(n), y=F(n +
> 1) and z>0 then z=F(n + 1).
>References G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers.
> 3rd ed., Oxford Univ. Press, London and New York, 1954, p. 148.
> V. E. Hoggatt, Jr., Fibonacci and Lucas Numbers. Houghton, Boston, MA,
> 1969.
> D. E. Knuth, The Art of Computer Programming. Addison-Wesley,
> Reading, MA, Vol. 1, p. 78.
> J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 288.
>Links: H. Bottomley and N. J. A. Sloane, Illustration of initial terms: the Fibonacci tree
> C. K. Caldwell, Fibonacci Numbers
> P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
> INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 9
> B. Kelly, Fibonacci and Lucas factorizations
> R. Knott, Fibonacci numbers with tables of F(0)-F(500)
> Hisanori Mishima, Factorizations of many number sequences
> E. W. Weisstein, Link to a section of The World of Mathematics.
> E. W. Weisstein, Link to a section of The World of Mathematics.
> E. W. Weisstein, Link to a section of The World of Mathematics.
> E. W. Weisstein, Link to a section of The World of Mathematics.
> Index entries for"core" sequences
>Formula: Paulo Ribenboim, The New Book of Prime Number Records, Springer, 1996.
> F(n) = ((1+sqrt(5))^n-(1-sqrt(5))^n)/(2^n*sqrt(5)). G.f.:
> x/(1-x-x^2).
> F(n+1) = SUM(0 < j <= [n/2]; binomial(n-j, j))
> [0 1; 1 1]^n [0 1] = [F(n); F(n+1)]
> x | F(n) ==> x | F(kn).
>Maple: with(combinat): A000045:=proc(n) fibonacci(n); end;
>Mma: Table[ Fibonacci[ k ],{k,1,50} ]
>Program: (PARI.2.0.11) a(n)=if(n<=1, n, a(n-1)+a(n-2));
> vector(35,n,a(n))
> (PARI) F(n)=round((1+sqrt(5))^n/2^n/sqrt(5))
> (PARI) F(n)=if(n<2,n>0,F(n-1)+F(n-2))
>See also: A000032(n)=A000045(n+1)+A000045(n-1), n>0. Cf. A060441.
> See also A000213, A000288, A000322, A000383, A060455.
>Keywords: core,nonn,easy,nice
>Offset: 0
>Author(s): njas
>
><font color="00FF00">Link: www.research.att.com/~njas/sequences/[/b]</font>
>Der Kerl hat da über 60k Zahlenreihen stehen. Wer sie alle aufrufen will, braucht Jahre. Aber vielleicht... ist ja noch was Schönes drunter?
>Gruß
>d.


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