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.

1, 1, 1, 2, 3, 5, 18, 325, 1512, 14365, 349272, 21734245, 276623424, 6933892901, 577589709312, 492757099009565, 16532350249637376, 1086038875887212525, 1240124656925798848512, 1450308695702968720107785

Offset

1,4

Links

Table of n, a(n) for n=1..20.

Formula

For n>=4, r(n) = -F(n)/(F(n-3) r(n-1)), where F(n) is the n-th Fibonacci number.

Example

The 5th Fibonacci number = 5 = 1 +1/(1 +1/(-2 +1/(3/2 -3/10))).
The 6th Fibonacci number = 8 = 1 +1/(1 +1/(-2 +1/(3/2 +1/(-10/3 +5/6)))).

Maple

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

Crossrefs

Cf. A128531.

Sequence in context: A042555 A041891 A042813 * A130076 A223704 A359940

Adjacent sequences: A128529 A128530 A128531 * A128533 A128534 A128535

Keyword

frac,nonn

Author

Leroy Quet, Mar 08 2007

Extensions

More terms from R. J. Mathar, Oct 09 2007

Status

approved