A041071 Denominators of continued fraction convergents to sqrt(42).

1, 2, 25, 52, 649, 1350, 16849, 35048, 437425, 909898, 11356201, 23622300, 294823801, 613269902, 7654062625, 15921395152, 198710804449, 413343004050, 5158826853049, 10730996710148, 133930787374825, 278592571459798, 3477041644892401, 7232675861244600

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: A248546 A369670 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