A042161 Denominators of continued fraction convergents to sqrt(605).

1, 1, 2, 5, 57, 62, 553, 615, 7318, 15251, 22569, 37820, 1837929, 1875749, 3713678, 9303105, 106047833, 115350938, 1028855337, 1144206275, 13615124362, 28374454999, 41989579361, 70364034360, 3419463228641, 3489827263001, 6909290491642, 17308408246285

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, 0, 0, 1860498, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^22 - x^21 + 2*x^20 - 5*x^19 + 57*x^18 - 62*x^17 + 553*x^16 - 615*x^15 + 7318*x^14 - 15251*x^13 + 22569*x^12 - 37820*x^11 - 22569*x^10 - 15251*x^9 - 7318*x^8 - 615*x^7 - 553*x^6 - 62*x^5 - 57*x^4 - 5*x^3 - 2*x^2 - x - 1) / ((x^4 - 11*x^2 - 1)*(x^4 + 11*x^2 - 1)*(x^8 - 11*x^6 + 122*x^4 + 11*x^2 + 1)*(x^8 + 11*x^6 + 122*x^4 - 11*x^2 + 1)). - Colin Barker, Dec 02 2013

a(n) = 1860498*a(n-12) - a(n-24) for n > 23. - Vincenzo Librandi, Jan 16 2014

Mathematica

Denominator[Convergents[Sqrt[605], 30]] (* Vincenzo Librandi, Jan 16 2014 *)

Crossrefs

Cf. A042160, A040580.

Sequence in context: A254406 A260654 A339167 * A176142 A101151 A138788

Adjacent sequences: A042158 A042159 A042160 * A042162 A042163 A042164

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Colin Barker, Dec 02 2013

Status

approved