A042747 Denominators of continued fraction convergents to sqrt(904).

1, 15, 901, 13530, 812701, 12204045, 733055401, 11008035060, 661215159001, 9929235420075, 596415340363501, 8956159340872590, 537965975792718901, 8078445796231656105, 485244713749692085201, 7286749152041612934120, 437690193836246468132401

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, 902, 0, -1).

Formula

a(0)=1, a(1)=15, a(2)=901, a(3)=13530, a(n)=902*a(n-2)-a(n-4). - Harvey P. Dale, Sep 25 2013

G.f.: -(x^2-15*x-1) / ((x^2-30*x-1)*(x^2+30*x-1)). - Colin Barker, Nov 19 2013

Mathematica

Denominator[Convergents[Sqrt[904], 30]] (* or *) LinearRecurrence[ {0, 902, 0, -1}, {1, 15, 901, 13530}, 30] (* Harvey P. Dale, Sep 25 2013 *)

Prog

(Magma) I:=[1, 15, 901, 13530]; [n le 4 select I[n] else 902*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Jan 28 2014

Crossrefs

Cf. A042746, A040873.

Sequence in context: A249963 A157462 A268166 * A324423 A261067 A136419

Adjacent sequences: A042744 A042745 A042746 * A042748 A042749 A042750

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

Additional term from Colin Barker, Nov 19 2013

Status

approved