A041655 Denominators of continued fraction convergents to sqrt(346).

1, 1, 2, 3, 5, 183, 188, 371, 559, 930, 34039, 34969, 69008, 103977, 172985, 6331437, 6504422, 12835859, 19340281, 32176140, 1177681321, 1209857461, 2387538782, 3597396243, 5984935025, 219055057143, 225039992168, 444095049311, 669135041479, 1113230090790

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, 186, 0, 0, 0, 0, 1).

Formula

G.f.: -(x^4-3*x^3+4*x^2-2*x+1)*(x^4+2*x^3+4*x^2+3*x+1) / (x^10+186*x^5-1). - Colin Barker, Nov 21 2013

a(n) = 186*a(n-5) + a(n-10) for n>9. - Vincenzo Librandi, Dec 22 2013

Mathematica

Denominator[Convergents[Sqrt[346], 30]] (* Harvey P. Dale, Nov 12 2013 *)
CoefficientList[Series[-(x^4 - 3 x^3 + 4 x^2 - 2 x + 1) (x^4 + 2 x^3 + 4 x^2 + 3 x + 1)/(x^10 + 186 x^5 - 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 22 2013 *)

Prog

(Magma) I:=[1, 1, 2, 3, 5, 183, 188, 371, 559, 930]; [n le 10 select I[n] else 186*Self(n-5)+Self(n-10): n in [1..40]]; // Vincenzo Librandi, Dec 22 2013

Crossrefs

Cf. A041654, A040327.

Sequence in context: A319609 A140551 A064936 * A082520 A062597 A038526

Adjacent sequences: A041652 A041653 A041654 * A041656 A041657 A041658

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 21 2013

Status

approved