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%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
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