A041581 Denominators of continued fraction convergents to sqrt(308).

1, 1, 2, 9, 11, 20, 691, 711, 1402, 6319, 7721, 14040, 485081, 499121, 984202, 4435929, 5420131, 9856060, 340526171, 350382231, 690908402, 3114015839, 3804924241, 6918940080, 239048886961, 245967827041, 485016714002, 2186034683049, 2671051397051

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,702,0,0,0,0,0,-1).

Formula

G.f.: -(x^4 -x^3 +2*x^2 +x +1)*(x^6 -10*x^3 -1) / ((x^4 -9*x^2 +1)*(x^8 +9*x^6 +80*x^4 +9*x^2 +1)). - Colin Barker, Nov 19 2013

a(n) = 702*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 20 2013

Mathematica

Denominator[Convergents[Sqrt[308], 30]] (* Harvey P. Dale, Nov 25 2011 *)
CoefficientList[Series[-(x^4 - x^3 + 2 x^2 + x + 1) (x^6 - 10 x^3 - 1)/((x^4 - 9 x^2 + 1) (x^8 + 9 x^6 + 80 x^4 + 9 x^2 + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 20 2013 *)

Prog

(Magma) I:=[1, 1, 2, 9, 11, 20, 691, 711, 1402, 6319, 7721, 14040]; [n le 12 select I[n] else 702*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 20 2013

Crossrefs

Cf. A041580, A040290.

Sequence in context: A131140 A022114 A041099 * A042463 A081613 A115911

Adjacent sequences: A041578 A041579 A041580 * A041582 A041583 A041584

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 19 2013

Status

approved