A128273 a(n) = the denominator 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, 3, 7, 171, 2401, 419121, 39647713, 47740815747, 30877916418391, 255080753983140651, 1130395777976404261441, 177322193432863810849593, 1944244855966235024678049078337, 754657638581703992960984555289787011

Offset

1,2

Comments

Limit_{n->oo} 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

A128273 := 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), denom(op(i, b))] ; od: RETURN(a) ; end: op(A128273(17)) ; # R. J. Mathar, Oct 08 2007

Crossrefs

Cf. A128272.

Sequence in context: A264931 A227890 A114789 * A105763 A291352 A132564

Adjacent sequences: A128270 A128271 A128272 * A128274 A128275 A128276

Keyword

frac,nonn,changed

Author

Leroy Quet, Feb 22 2007

Extensions

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

Status

approved