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A041834 Numerators of continued fraction convergents to sqrt(438). 2
20, 21, 272, 293, 11992, 12285, 159412, 171697, 7027292, 7198989, 93415160, 100614149, 4117981120, 4218595269, 54741124348, 58959719617, 2413129909028, 2472089628645, 32078205452768, 34550295081413 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
FORMULA
G.f.: -(x^7-20*x^6+21*x^5-272*x^4-293*x^3-272*x^2-21*x-20)/(x^8-586*x^4+1). - Vincenzo Librandi, Nov 10 2013
a(n) = 586*a(n-4)-a(n-8). - Vincenzo Librandi, Nov 10 2013
MATHEMATICA
Numerator[Convergents[Sqrt[438], 30]] (* or *) CoefficientList[Series[-(x^7 - 20 x^6 + 21 x^5 - 272 x^4 - 293 x^3 - 272 x^2 - 21 x - 20)/(x^8 - 586 x^4 + 1), {x, 0, 25}], x] (* Vincenzo Librandi, Nov 10 2013 *)
PROG
(Magma) I:=[20, 21, 272, 293, 11992, 12285, 159412, 171697]; [n le 8 select I[n] else 586*Self(n-4)-Self(n-8): n in [1..25]]; // Vincenzo Librandi, Nov 10 2013
CROSSREFS
Cf. A041835.
Sequence in context: A041830 A041832 A082260 * A219798 A063013 A028931
KEYWORD
nonn,cofr,frac,easy,less
AUTHOR
STATUS
approved

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Last modified March 29 11:45 EDT 2024. Contains 371278 sequences. (Running on oeis4.)