Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #10 Aug 18 2015 00:13:55
%S 1,1,15,77,5301,189679,87596289,21608003585,68221625702463,
%T 115452529488363949,2497495662248930113941,80258100236324702562311,
%U 4295613290302749695769359713665,341566880541004135370464340131322497
%N 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.
%C limit{n -> inf} b(n)*b(n+1) = 1.
%e b(n): 1, 1/3, 15/7, 77/171, 5301/2401,...
%e 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)).
%e 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)).
%p 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
%Y Cf. A128273.
%K frac,nonn
%O 1,3
%A _Leroy Quet_, Feb 22 2007
%E More terms from _R. J. Mathar_, Oct 08 2007