A057677 - OEIS

A057677

a(n) is the numerator of b(n) where b(n)=1/b(n-1)+1/b(n-2) with b(1)=1 and b(2)=2.

1, 2, 3, 7, 32, 339, 14287, 6877760, 143806067571, 1372321205281802503, 277081140489649960447116859520, 544875880027767543589801386360499677678401262339

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..12.

FORMULA

a(n) satisfies the cubic recurrence : a(1)=1, a(2)=2, a(3)=3, a(4)=7, a(5)=32 and for n>=6 a(n)=a(n-2)^2*a(n-3)+a(n-1)*a(n-3)*a(n-4).

Limit_{n->oo} b(n)=sqrt(2) with geometric convergence since abs(b(n)-sqrt(2))<2*2^(-n/2).

CROSSREFS

Cf. A066932 (denominators).

Sequence in context: A066279 A337221 A161471 * A032148 A101484 A004026

Adjacent sequences: A057674 A057675 A057676 * A057678 A057679 A057680

KEYWORD

nonn,frac

AUTHOR

Zak Seidov, Oct 24 2002

EXTENSIONS

Edited by Benoit Cloitre, Oct 25 2005

STATUS

approved