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A041071 Denominators of continued fraction convergents to sqrt(42). 2
1, 2, 25, 52, 649, 1350, 16849, 35048, 437425, 909898, 11356201, 23622300, 294823801, 613269902, 7654062625, 15921395152, 198710804449, 413343004050, 5158826853049, 10730996710148, 133930787374825, 278592571459798, 3477041644892401, 7232675861244600 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (0,26,0,-1).

FORMULA

G.f.: -(x^2-2*x-1) / (x^4-26*x^2+1). - Colin Barker, Nov 12 2013

a(n) = 26*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 10 2013

MATHEMATICA

Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[42], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 22 2011 *)

Denominator[Convergents[Sqrt[42], 30]] (* Vincenzo Librandi, Dec 10 2013 *)

LinearRecurrence[{0, 26, 0, -1}, {1, 2, 25, 52}, 30] (* Harvey P. Dale, Oct 17 2019 *)

PROG

(MAGMA) I:=[1, 2, 25, 52]; [n le 4 select I[n] else 26*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 10 2013

CROSSREFS

Cf. A041070.

Sequence in context: A054292 A248546 A038834 * A153478 A226491 A062933

Adjacent sequences:  A041068 A041069 A041070 * A041072 A041073 A041074

KEYWORD

nonn,cofr,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Colin Barker, Nov 12 2013

STATUS

approved

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Last modified November 19 18:39 EST 2019. Contains 329323 sequences. (Running on oeis4.)