|
|
A041047
|
|
Denominators of continued fraction convergents to sqrt(29).
|
|
11
|
|
|
1, 2, 3, 5, 13, 135, 283, 418, 701, 1820, 18901, 39622, 58523, 98145, 254813, 2646275, 5547363, 8193638, 13741001, 35675640, 370497401, 776670442, 1147167843, 1923838285, 4994844413, 51872282415
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
The terms of this sequence can be constructed with the terms of sequence A052918.
For the terms of the periodical sequence of the continued fraction for sqrt(29) see A010128. We observe that its period is five. The decimal expansion of sqrt(29) is A010484. - Johannes W. Meijer, Jun 12 2010
|
|
LINKS
|
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,140,0,0,0,0,1).
|
|
FORMULA
|
G.f.: (1 + 2*x + 3*x^2 + 5*x^3 + 13*x^4 - 5*x^5 + 3*x^6 - 2*x^7 + x^8)/(1 - 140*x^5 - x^10). - Peter J. C. Moses, Jul 29 2013
|
|
MATHEMATICA
|
|
|
PROG
|
(Magma) I:=[1, 2, 3, 5, 13, 135, 283, 418, 701, 1820]; [n le 10 select I[n] else 140*Self(n-5)+Self(n-10): n in [1..50]]; // Vincenzo Librandi, Dec 10 2013
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,cofr,frac,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|