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

verfasst von dottore, 21.05.2001, 16:01

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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