A041885 Denominators of continued fraction convergents to sqrt(464).

1, 1, 2, 11, 13, 24, 37, 209, 246, 455, 19356, 19811, 39167, 215646, 254813, 470459, 725272, 4096819, 4822091, 8918910, 379416311, 388335221, 767751532, 4227092881, 4994844413, 9221937294, 14216781707, 80305845829, 94522627536, 174828473365, 7437318508866

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, 19602, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^18 -x^17 +2*x^16 -11*x^15 +13*x^14 -24*x^13 +37*x^12 -209*x^11 +246*x^10 -455*x^9 -246*x^8 -209*x^7 -37*x^6 -24*x^5 -13*x^4 -11*x^3 -2*x^2 -x -1) / ((x^10 -140*x^5 -1)*(x^10 +140*x^5 -1)). - Colin Barker, Nov 26 2013

a(n) = 19602*a(n-10) - a(n-20) for n>19. - Vincenzo Librandi, Dec 26 2013

Mathematica

Denominator[Convergents[Sqrt[464], 30]] (* Vincenzo Librandi, Dec 26 2013 *)

Prog

(Magma) I:=[1, 1, 2, 11, 13, 24, 37, 209, 246, 455, 19356, 19811, 39167, 215646, 254813, 470459, 725272, 4096819, 4822091, 8918910]; [n le 20 select I[n] else 19602*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 26 2013

Crossrefs

Cf. A041884, A040442.

Sequence in context: A363215 A022115 A042453 * A247338 A154742 A257329

Adjacent sequences: A041882 A041883 A041884 * A041886 A041887 A041888

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 26 2013

Status

approved