A041693 Denominators of continued fraction convergents to sqrt(366).

1, 7, 8, 15, 23, 61, 755, 1571, 2326, 3897, 6223, 47458, 1809627, 12714847, 14524474, 27239321, 41763795, 110766911, 1370966727, 2852700365, 4223667092, 7076367457, 11300034549, 86176609300, 3286011187949, 23088254924943, 26374266112892, 49462521037835

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, 0, 0, 0, 0, 0, 0, 1815850, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^22 -7*x^21 +8*x^20 -15*x^19 +23*x^18 -61*x^17 +755*x^16 -1571*x^15 +2326*x^14 -3897*x^13 +6223*x^12 -47458*x^11 -6223*x^10 -3897*x^9 -2326*x^8 -1571*x^7 -755*x^6 -61*x^5 -23*x^4 -15*x^3 -8*x^2 -7*x-1)/(x^24 -1815850*x^12 +1). - Vincenzo Librandi, Dec 23 2013

a(n) = 1815850*a(n-12) - a(n-24) for n>23. - Vincenzo Librandi, Dec 23 2013

Mathematica

Denominator[Convergents[Sqrt[366], 30]] (* or *) CoefficientList[Series[-(x^22 - 7 x^21 + 8 x^20 - 15 x^19 + 23 x^18 - 61 x^17 + 755 x^16 - 1571 x^15 + 2326 x^14 - 3897 x^13 + 6223 x^12 - 47458 x^11 - 6223 x^10 - 3897 x^9 - 2326 x^8 - 1571 x^7 - 755 x^6 - 61 x^5 - 23 x^4 - 15 x^3 - 8 x^2 - 7 x - 1)/(x^24 - 1815850 x^12 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 23 2013 *)

Prog

(Magma) I:=[1, 7, 8, 15, 23, 61, 755, 1571, 2326, 3897, 6223, 47458, 1809627, 12714847, 14524474, 27239321, 41763795, 110766911, 1370966727, 2852700365, 4223667092, 7076367457, 11300034549, 86176609300]; [n le 24 select I[n] else 1815850*Self(n-12)-Self(n-24): n in [1..40]]; // Vincenzo Librandi, Dec 23 2013

Crossrefs

Cf. A041692.

Sequence in context: A022097 A041100 A129658 * A042001 A020690 A191413

Adjacent sequences: A041690 A041691 A041692 * A041694 A041695 A041696

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Dec 23 2013

Status

approved