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

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

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).

Crossrefs

Cf. A010496, A040035, A041070 (numerators).

Programs

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

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 *)

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

Extensions

More terms from Colin Barker, Nov 12 2013