A128272 a(n) = the numerator of b(n): {b(n)} is such that the continued fraction (of rational terms) [b(1);b(2),...,b(n)] equals the F(n+1)^2/F(n)^2, for every positive integer n, where F(n) is the n-th Fibonacci number.

1, 1, 15, 77, 5301, 189679, 87596289, 21608003585, 68221625702463, 115452529488363949, 2497495662248930113941, 80258100236324702562311, 4295613290302749695769359713665, 341566880541004135370464340131322497

Offset

1,3

Comments

limit{n -> inf} b(n)*b(n+1) = 1.

Links

Table of n, a(n) for n=1..14.

Example

b(n): 1, 1/3, 15/7, 77/171, 5301/2401,...
F(5)^2/F(4)^2 = 25/9 equals [b(1);b(2),b(3),b(4)] = 1 +1/(1/3 +1/(15/7 +171/77)).
F(6)^2/F(5)^2 = 64/25 equals [b(1);b(2),b(3),b(4),b(5)] = 1 +1/(1/3 +1/(15/7 +1/(77/171 +2401/5301)).

Maple

A128272 := proc(nmax) local a, b, i, n, ffrac ; b := [1] ; while nops(b) < nmax do n := nops(b)+1 ; ffrac := (combinat[fibonacci](n+1)/combinat[fibonacci](n))^2 ; for i from 1 to n-1 do ffrac := 1/(ffrac-b[i]) ; od: b := [op(b), ffrac] ; od: a := [] ; for i from 1 to nops(b) do a := [op(a), numer(op(i, b))] ; od: RETURN(a) ; end: op(A128272(14)) ; # R. J. Mathar, Oct 08 2007

Crossrefs

Cf. A128273.

Sequence in context: A205433 A303097 A374219 * A180579 A081591 A269620

Adjacent sequences: A128269 A128270 A128271 * A128273 A128274 A128275

Keyword

frac,nonn

Author

Leroy Quet, Feb 22 2007

Extensions

More terms from R. J. Mathar, Oct 08 2007

Status

approved