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A042326
Numerators of continued fraction convergents to sqrt(690).
2
26, 79, 105, 289, 394, 1471, 76886, 232129, 309015, 850159, 1159174, 4327681, 226198586, 682923439, 909122025, 2501167489, 3410289514, 12732036031, 665476163126, 2009160525409, 2674636688535, 7358433902479
OFFSET
0,1
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,2942,0,0,0,0,0,-1).
FORMULA
G.f.: -(x^11 -26*x^10 +79*x^9 -105*x^8 +289*x^7 -394*x^6 -1471*x^5 -394*x^4 -289*x^3 -105*x^2 -79*x -26)/(x^12 -2942*x^6 +1). - Vincenzo Librandi Nov 21 2013
a(n) = 2942*a(n-6) - a(n-12). - Vincenzo Librandi, Nov 21 2013
MATHEMATICA
Numerator[Convergents[Sqrt[690], 30]] (* or *) CoefficientList[Series[-(x^11 - 26 x^10 + 79 x^9 - 105 x^8 + 289 x^7 - 394 x^6 - 1471 x^5 - 394 x^4 - 289 x^3 - 105 x^2 - 79 x - 26)/(x^12 - 2942 x^6 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 21 2013 *)
PROG
(Magma) I:=[26, 79, 105, 289, 394, 1471, 76886, 232129, 309015, 850159, 1159174, 4327681]; [n le 12 select I[n] else 2942*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Nov 21 2013
CROSSREFS
Cf. A042327.
Sequence in context: A126380 A083578 A173307 * A042328 A042330 A052241
KEYWORD
nonn,cofr,frac,easy
AUTHOR
STATUS
approved