|
Search: id:A128532
|
|
|
| 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. |
|
+0
2
|
|
| 1, 1, 1, 2, 3, 5, 18, 325, 1512, 14365, 349272, 21734245, 276623424, 6933892901, 577589709312, 492757099009565, 16532350249637376, 1086038875887212525, 1240124656925798848512, 1450308695702968720107785
(list; graph; listen)
|
|
|
OFFSET
|
1,4
|
|
|
LINKS
|
Leroy Quet, Home Page (listed in lieu of email address)
|
|
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 (mathar(AT)strw.leidenuniv.nl), Oct 09 2007
|
|
CROSSREFS
|
Cf. A128531.
Sequence in context: A042555 A041891 A042813 this_sequence A130076 A090116 A038876
Adjacent sequences: A128529 A128530 A128531 this_sequence A128533 A128534 A128535
|
|
KEYWORD
|
frac,nonn
|
|
AUTHOR
|
Leroy Quet Mar 08 2007
|
|
EXTENSIONS
|
More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 09 2007
|
|
|
Search completed in 0.002 seconds
|
