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A041551
Denominators of continued fraction convergents to sqrt(293).
10
1, 8, 9, 17, 145, 4947, 39721, 44668, 84389, 719780, 24556909, 197175052, 221731961, 418907013, 3572988065, 121900501223, 978776997849, 1100677499072, 2079454496921, 17736313474440, 605114112627881, 4858649214497488, 5463763327125369, 10322412541622857
OFFSET
0,2
COMMENTS
The a(n) terms of this sequence can be constructed with the terms of sequence A178765. For the terms of the periodical sequence of the continued fraction for sqrt(293) see A040275. We observe that its period is five. - Johannes W. Meijer, Jun 12 2010
LINKS
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 4964, 0, 0, 0, 0, 1).
FORMULA
a(5n) = A178765(3n), a(5n+1) = (A178765(3n+1) - A178765(3n))/2, a(5n+2) = (A178765(3n+1) + A178765(3n))/2, a(5n+3) = A178765(3n+1) and a(5n+4) = A178765(3n+2)/2. - Johannes W. Meijer, Jun 12 2010
G.f.: -(x^8-8*x^7+9*x^6-17*x^5+145*x^4+17*x^3+9*x^2+8*x+1) / (x^10+4964*x^5-1). - Colin Barker, Nov 12 2013
a(n) = 4964*a(n-5) + a(n-10) for n>9. - Vincenzo Librandi, Dec 20 2013
MATHEMATICA
Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[293], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Jun 23 2011 *)
Denominator[Convergents[Sqrt[293 ], 30]] (* Vincenzo Librandi, Dec 20 2013 *)
PROG
(Magma) I:=[1, 8, 9, 17, 145, 4947, 39721, 44668, 84389, 719780]; [n le 10 select I[n] else 4964*Self(n-5)+Self(n-10): n in [1..40]]; // Vincenzo Librandi, Dec 20 2013
KEYWORD
nonn,frac,easy
AUTHOR
STATUS
approved