A041599 Denominators of continued fraction convergents to sqrt(317).

1, 1, 5, 41, 46, 133, 312, 445, 3872, 15933, 19805, 689303, 709108, 3525735, 28914988, 32440723, 93796434, 220033591, 313830025, 2730673791, 11236525189, 13967198980, 486121290509, 500088489489, 2486475248465, 20391890477209, 22878365725674, 66148621928557

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,705236,0,0,0,0,0,0,0,0,0,0,1).

Formula

G.f.: -(x^20 -x^19 +5*x^18 -41*x^17 +46*x^16 -133*x^15 +312*x^14 -445*x^13 +3872*x^12 -15933*x^11 +19805*x^10 +15933*x^9 +3872*x^8 +445*x^7 +312*x^6 +133*x^5 +46*x^4 +41*x^3 +5*x^2 +x +1) / (x^22 +705236*x^11 -1). - Colin Barker, Nov 19 2013

a(n) = 705236*a(n-11) + a(n-22) for n>21. - Vincenzo Librandi, Dec 21 2013

Mathematica

Denominator[Convergents[Sqrt[317], 30]] (* Vincenzo Librandi Dec 21 2013 *)

Prog

(Magma) I:=[1, 1, 5, 41, 46, 133, 312, 445, 3872, 15933, 19805, 689303, 709108, 3525735, 28914988, 32440723, 93796434, 220033591, 313830025, 2730673791, 11236525189, 13967198980]; [n le 22 select I[n] else 705236*Self(n-11)+Self(n-22): n in [1..40]]; // Vincenzo Librandi, Dec 21 2013

Crossrefs

Cf. A041598, A040299.

Sequence in context: A010573 A326265 A043083 * A302692 A232881 A174054

Adjacent sequences: A041596 A041597 A041598 * A041600 A041601 A041602

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 19 2013

Status

approved