A113500 Maximum element in the continued fraction for F(5n+3)^5/F(5n+2)^5 where F=A000045 are Fibonacci numbers.

32, 3042, 375131, 46137317, 5674515856, 697919312217, 85838400887831, 10557425389890242, 1298477484555612931, 159702173174950499517, 19642068823034355828656, 2415814763060050816424417

Offset

0,1

References

B. Cloitre, On rational sequences yielding continued fractions with unbounded coefficients, in preparation

Links

Table of n, a(n) for n=0..11.

G. C. Greubel, Table of n, a(n) for n = 0..475

Formula

a(n) = 2*L(10*n+4) + L(10*n+5) + (-1)^n*7 - 1, where L(k) denotes the k-th Lucas number L(k) = F(k-1) + F(k+1), for n >= 0.

Empirical g.f.: (x^4-140*x^3-965*x^2+894*x-32) / ((x-1)*(x+1)*(x^2-123*x+1)). - Colin Barker, Jun 17 2013

Mathematica

Table[2*LucasL[10*n + 4] + LucasL[10*n + 5] + 7*(-1)^n - 1, {n, 0, 50}] (* G. C. Greubel, Mar 13 2017 *)

Prog

(PARI) a(n)=vecmax(contfrac(fibonacci(5*n+3)^5/fibonacci(5*n+2)^5))

Crossrefs

Cf. A000045.

Sequence in context: A248074 A220299 A264115 * A064018 A067321 A104652

Adjacent sequences: A113497 A113498 A113499 * A113501 A113502 A113503

Keyword

nonn

Author

Benoit Cloitre, Jan 10 2006

Status

approved