A041875 Denominators of continued fraction convergents to sqrt(459).

1, 2, 5, 7, 33, 700, 2833, 3533, 9899, 23331, 989801, 2002933, 4995667, 6998600, 32990067, 699790007, 2832150095, 3531940102, 9896030299, 23324000700, 989504059699, 2002332120098, 4994168299895, 6996500419993, 32980169979867, 699580069997200

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, 0, 0, 0, 0, 0, 0, 0, 0, 999700, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^18 -2*x^17 +5*x^16 -7*x^15 +33*x^14 -700*x^13 +2833*x^12 -3533*x^11 +9899*x^10 -23331*x^9 -9899*x^8 -3533*x^7 -2833*x^6 -700*x^5 -33*x^4 -7*x^3 -5*x^2 -2*x -1) / (x^20 -999700*x^10 +1). - Colin Barker, Nov 26 2013

a(n) = 999700*a(n-10) - a(n-20) for n>19. - Vincenzo Librandi, Dec 26 2013

Mathematica

Denominator[Convergents[Sqrt[459], 30]] (* Vincenzo Librandi, Dec 26 2013 *)

Prog

(Magma) I:=[1, 2, 5, 7, 33, 700, 2833, 3533, 9899, 23331, 989801, 2002933, 4995667, 6998600, 32990067, 699790007, 2832150095, 3531940102, 9896030299, 23324000700]; [n le 20 select I[n] else 999700*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 26 2013

Crossrefs

Cf. A041874, A040437.

Sequence in context: A056443 A042931 A085394 * A072188 A277056 A160621

Adjacent sequences: A041872 A041873 A041874 * A041876 A041877 A041878

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 26 2013

Status

approved