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A041073 Denominators of continued fraction convergents to sqrt(43). 2
1, 1, 2, 7, 9, 52, 61, 235, 296, 531, 6668, 7199, 13867, 48800, 62667, 362135, 424802, 1636541, 2061343, 3697884, 46435951, 50133835, 96569786, 339843193, 436412979, 2521908088, 2958321067, 11396871289, 14355192356, 25752063645, 323379956096, 349132019741 (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 (0,0,0,0,0,0,0,0,0,6964,0,0,0,0,0,0,0,0,0,-1).

FORMULA

G.f.: -(x^18 -x^17 +2*x^16 -7*x^15 +9*x^14 -52*x^13 +61*x^12 -235*x^11 +296*x^10 -531*x^9 -296*x^8 -235*x^7 -61*x^6 -52*x^5 -9*x^4 -7*x^3 -2*x^2 -x -1) / (x^20 -6964*x^10 +1). - Colin Barker, Nov 12 2013

a(n) = 6964*a(n-10) - a(n-20). - Vincenzo Librandi, Dec 10 2013

MATHEMATICA

Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[43], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 22 2011 *)

Denominator[Convergents[Sqrt[43], 40]] (* Vincenzo Librandi, Dec 10 2013 *)

PROG

(MAGMA) I:=[1, 1, 2, 7, 9, 52, 61, 235, 296, 531, 6668, 7199, 13867, 48800, 62667, 362135, 424802, 1636541, 2061343, 3697884]; [n le 20 select I[n] else 6964*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 10 2013

CROSSREFS

Cf. A010497, A041072.

Sequence in context: A042063 A041717 A002353 * A079942 A272412 A042561

Adjacent sequences:  A041070 A041071 A041072 * A041074 A041075 A041076

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Colin Barker, Nov 12 2013

STATUS

approved

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Last modified December 12 07:00 EST 2019. Contains 329948 sequences. (Running on oeis4.)