A110953 Starting a priori with the fraction 1/1, the denominators of fractions built according to the rule: add top and bottom to get the new bottom, add top and 9 times the bottom to get the new top.

2, 12, 40, 176, 672, 2752, 10880, 43776, 174592, 699392, 2795520, 11186176, 44736512, 178962432, 715816960, 2863333376, 11453202432, 45813071872, 183251763200, 733008101376

Offset

1,1

Comments

The limit of the sequence of fractions used to generate this sequence is 3.

Essentially the same as A003683. - R. J. Mathar, May 25 2009

References

Prime Obsession, John Derbyshire, Joseph Henry Press, April 2004, p. 16.

Links

Table of n, a(n) for n=1..20.

Formula

Given a(0)=1, b(0)=1 then for i>=1, a(i)/b(i) = (a(i-1)+ 9*b(i-1)) / (a(i-1) + b(i-1)).

Prog

(PARI) g(n, k, typ) = /* typ = 1 numerator, 2 denominator, k = multiple of denom */ { local(a, b, x, tmp); a=1; b=1; for(x=1, n, tmp=b; b=a+b; a=k*tmp+a; if(typ==1, print1(a", "), print1(b", ")) ); print(); print(a/b+.) }

Crossrefs

Sequence in context: A074447 A190064 A240122 * A003683 A188572 A098519

Adjacent sequences: A110950 A110951 A110952 * A110954 A110955 A110956

Keyword

easy,nonn

Author

Cino Hilliard, Sep 25 2005

Status

approved