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A041223
Denominators of continued fraction convergents to sqrt(123).
2
1, 11, 243, 2684, 59291, 654885, 14466761, 159789256, 3529830393, 38987923579, 861264149131, 9512893564020, 210144922557571, 2321107041697301, 51274499839898193, 566340605280577424, 12510767816012601521, 138184786581419194155, 3052576072607234872931
OFFSET
0,2
FORMULA
G.f.: (1 + 11*x - x^2)/(1 - 244*x^2 + x^4). - Vincenzo Librandi, Dec 13 2013
a(n) = 244*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 13 2013
MATHEMATICA
Denominator[Convergents[Sqrt[123], 30]] (* or *) CoefficientList[Series[(1 + 11 x - x^2)/(1 - 244 x^2 + x^4), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 13 2013 *)
LinearRecurrence[{0, 244, 0, -1}, {1, 11, 243, 2684}, 20] (* Harvey P. Dale, Jul 27 2015 *)
PROG
(Magma) I:=[1, 11, 243, 2684]; [n le 4 select I[n] else 244*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 13 2013
CROSSREFS
Cf. A041222.
Sequence in context: A196258 A121826 A377448 * A041220 A347483 A219089
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, Dec 13 2012
STATUS
approved