A041707 Denominators of continued fraction convergents to sqrt(373).

1, 3, 16, 83, 265, 10153, 30724, 163773, 849589, 2712540, 103926109, 314490867, 1676380444, 8696393087, 27765559705, 1063787661877, 3219128545336, 17159430388557, 89016280488121, 284208271852920, 10888930610899081, 32951000104550163, 175643931133649896

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, 10236, 0, 0, 0, 0, 1).

Formula

G.f.: -(x^8 -3*x^7 +16*x^6 -83*x^5 +265*x^4 +83*x^3 +16*x^2 +3*x +1) / (x^10 +10236*x^5 -1). - Colin Barker, Nov 22 2013

a(n) = 10236*a(n-5) + a(n-10) for n>9. - Vincenzo Librandi, Dec 23 2013

Mathematica

Denominator[Convergents[Sqrt[373], 30]] (* Vincenzo Librandi, Dec 23 2013 *)

Prog

(Magma) I:=[1, 3, 16, 83, 265, 10153, 30724, 163773, 849589, 2712540]; [n le 10 select I[n] else 10236*Self(n-5)+Self(n-10): n in [1..40]]; // Vincenzo Librandi, Dec 23 2013

Crossrefs

Cf. A041706, A040353.

Sequence in context: A037780 A163012 A164100 * A037584 A030983 A069429

Adjacent sequences: A041704 A041705 A041706 * A041708 A041709 A041710

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 22 2013

Status

approved