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A041651 Denominators of continued fraction convergents to sqrt(344). 2
1, 1, 2, 9, 11, 42, 53, 254, 307, 561, 20503, 21064, 41567, 187332, 228899, 874029, 1102928, 5285741, 6388669, 11674410, 426667429, 438341839, 865009268, 3898378911, 4763388179, 18188543448, 22951931627, 109996269956, 132948201583, 242944471539 (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, 0, 0, 0, 0, 20810, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

FORMULA

G.f.: -(x^18 -x^17 +2*x^16 -9*x^15 +11*x^14 -42*x^13 +53*x^12 -254*x^11 +307*x^10 -561*x^9 -307*x^8 -254*x^7 -53*x^6 -42*x^5 -11*x^4 -9*x^3 -2*x^2 -x -1) / (x^20 -20810*x^10 +1). - Colin Barker, Nov 20 2013

a(n) = 20810*a(n-10) - a(n-20) for n>19. - Vincenzo Librandi, Dec 22 2013

MATHEMATICA

Denominator[Convergents[Sqrt[344], 30]] (* Vincenzo Librandi, Dec 22 2013 *)

PROG

(MAGMA) I:=[1, 1, 2, 9, 11, 42, 53, 254, 307, 561, 20503, 21064, 41567, 187332, 228899, 874029, 1102928, 5285741, 6388669, 11674410]; [n le 20 select I[n] else 20810*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 22 2013

CROSSREFS

Cf. A041650, A040325.

Sequence in context: A042053 A134775 A042573 * A042687 A083159 A041335

Adjacent sequences:  A041648 A041649 A041650 * A041652 A041653 A041654

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Colin Barker, Nov 20 2013

STATUS

approved

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Last modified July 15 20:00 EDT 2019. Contains 325056 sequences. (Running on oeis4.)