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A041833 Denominators of continued fraction convergents to sqrt(437). 3
1, 1, 10, 21, 199, 220, 8999, 9219, 91970, 193159, 1830401, 2023560, 82772801, 84796361, 845940050, 1776676461, 16836028199, 18612704660, 761344214599, 779956919259, 7780956487930, 16341869895119, 154857785544001, 171199655439120, 7002844003108801 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 9198, 0, 0, 0, 0, 0, -1).

FORMULA

G.f.: -(x^10 -x^9 +10*x^8 -21*x^7 +199*x^6 -220*x^5 -199*x^4 -21*x^3 -10*x^2 -x -1) / ((x^4 -21*x^2 +1)*(x^8 +21*x^6 +440*x^4 +21*x^2 +1)). - Colin Barker, Nov 25 2013

a(n) = 9198*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 25 2013

MATHEMATICA

Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[437], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Jun 23 2011 *)

Denominator[Convergents[Sqrt[437], 30]] (* Vincenzo Librandi, Dec 25 2013 *)

PROG

(MAGMA) I:=[1, 1, 10, 21, 199, 220, 8999, 9219, 91970, 193159, 1830401, 2023560]; [n le 12 select I[n] else 9198*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 25 2013

CROSSREFS

Cf. A041832, A040416.

Sequence in context: A177131 A177180 A275248 * A153317 A110418 A041198

Adjacent sequences:  A041830 A041831 A041832 * A041834 A041835 A041836

KEYWORD

nonn,easy,frac

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified February 24 01:11 EST 2020. Contains 332195 sequences. (Running on oeis4.)