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A128532 a(n) = denominator of r(n): r(n) is such that the continued fraction (of rational terms) [r(1);r(2),...r(n)] equals the n-th Fibonacci number, for every positive integer n.

%I A128532 #10 Aug 18 2015 00:18:21
%S A128532 1,1,1,2,3,5,18,325,1512,14365,349272,21734245,276623424,6933892901,
%T A128532 577589709312,492757099009565,16532350249637376,1086038875887212525,
%U A128532 1240124656925798848512,1450308695702968720107785
%N A128532 a(n) = denominator of r(n): r(n) is such that the continued fraction (of rational terms) [r(1);r(2),...r(n)] equals the n-th Fibonacci number, for every positive integer n.
%F A128532 For n>=4, r(n) = -F(n)/(F(n-3) r(n-1)), where F(n) is the n-th Fibonacci number.
%e A128532 The 5th Fibonacci number = 5 = 1 +1/(1 +1/(-2 +1/(3/2 -3/10))).
%e A128532 The 6th Fibonacci number = 8 = 1 +1/(1 +1/(-2 +1/(3/2 +1/(-10/3 +5/6)))).
%p A128532 L2cfrac := proc(L,targ) local a,i; a := targ ; for i from 1 to nops(L) do a := 1/(a-op(i,L)) ; od: end: A128532 := proc(nmax) local b,n,bnxt; b := [1] ; for n from nops(b)+1 to nmax do bnxt := L2cfrac(b,combinat[fibonacci](n+1)) ; b := [op(b),bnxt] ; od: [seq( denom(b[i]),i=1..nops(b))] ; end: A128532(22) ; # _R. J. Mathar_, Oct 09 2007
%Y A128532 Cf. A128531.
%K A128532 frac,nonn
%O A128532 1,4
%A A128532 _Leroy Quet_, Mar 08 2007
%E A128532 More terms from _R. J. Mathar_, Oct 09 2007