OFFSET
1,3
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: A128531 := 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( numer(b[i]), i=1..nops(b))] ; end: A128531(22) ; # R. J. Mathar, Oct 09 2007
MATHEMATICA
r[n_] := r[n] = Switch[n, 1, 1, 2, 1, 3, -2, _, -Fibonacci[n]/(Fibonacci[n-3]*r[n-1])];
a[n_] := Numerator[r[n]];
Table[a[n], {n, 1, 21}] (* Jean-François Alcover, Sep 24 2024 *)
CROSSREFS
KEYWORD
frac,sign
AUTHOR
Leroy Quet, Mar 08 2007
EXTENSIONS
More terms from R. J. Mathar, Oct 09 2007
STATUS
approved