A041557 Denominators of continued fraction convergents to sqrt(296).

1, 4, 5, 39, 44, 215, 7354, 29631, 36985, 288526, 325511, 1590570, 54404891, 219210134, 273615025, 2134515309, 2408130334, 11767036645, 402487376264, 1621716541701, 2024203917965, 15791143967456, 17815347885421, 87052535509140, 2977601555196181

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,7398,0,0,0,0,0,-1).

Formula

G.f.: -(x^10 -4*x^9 +5*x^8 -39*x^7 +44*x^6 -215*x^5 -44*x^4 -39*x^3 -5*x^2 -4*x -1) / ((x^6 -86*x^3 -1)*(x^6 +86*x^3 -1)). - Colin Barker, Nov 19 2013

a(n) = 7398*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 20 2013

Mathematica

Denominator[Convergents[Sqrt[296], 40]] (* Harvey P. Dale, Jan 13 2012 *)
CoefficientList[Series[-(x^10 - 4 x^9 + 5 x^8 - 39 x^7 + 44 x^6 - 215 x^5 - 44 x^4 - 39 x^3 - 5 x^2 - 4 x - 1)/((x^6 - 86 x^3 - 1) (x^6 + 86 x^3 - 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 20 2013 *)

Prog

(Magma) I:=[1, 4, 5, 39, 44, 215, 7354, 29631, 36985, 288526, 325511, 1590570]; [n le 12 select I[n] else 7398*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 20 2013

Crossrefs

Cf. A041556, A040278.

Sequence in context: A152291 A336024 A228798 * A270087 A265689 A270098

Adjacent sequences: A041554 A041555 A041556 * A041558 A041559 A041560

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 19 2013

Status

approved