A041739 Denominators of continued fraction convergents to sqrt(389).

1, 1, 3, 4, 7, 11, 18, 47, 65, 2517, 2582, 7681, 10263, 17944, 28207, 46151, 120509, 166660, 6453589, 6620249, 19694087, 26314336, 46008423, 72322759, 118331182, 308985123, 427316305, 16547004713, 16974321018, 50495646749, 67469967767, 117965614516

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, 2564, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Formula

G.f.: -(x^16 -x^15 +3*x^14 -4*x^13 +7*x^12 -11*x^11 +18*x^10 -47*x^9 +65*x^8 +47*x^7 +18*x^6 +11*x^5 +7*x^4 +4*x^3 +3*x^2 +x +1) / (x^18 +2564*x^9 -1). - Colin Barker, Nov 23 2013

Mathematica

Denominator[Convergents[Sqrt[389], 30]] (* Vincenzo Librandi, Dec 23 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 2564, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {1, 1, 3, 4, 7, 11, 18, 47, 65, 2517, 2582, 7681, 10263, 17944, 28207, 46151, 120509, 166660}, 40] (* Harvey P. Dale, Aug 05 2025 *)

Crossrefs

Cf. A041738, A040369.

Sequence in context: A024319 A041209 A293420 * A042593 A041018 A378275

Adjacent sequences: A041736 A041737 A041738 * A041740 A041741 A041742

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Colin Barker, Nov 23 2013

Status

approved