A041701 Denominators of continued fraction convergents to sqrt(370).

1, 4, 17, 650, 2617, 11118, 425101, 1711522, 7271189, 278016704, 1119338005, 4755368724, 181823349517, 732048766792, 3110018416685, 118912748600822, 478761012819973, 2033956799880714, 77769119408287105, 313110434433029134, 1330210857140403641

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,654,0,0,1).

Formula

G.f.: -(x^4-4*x^3+17*x^2+4*x+1) / (x^6+654*x^3-1). - Colin Barker, Nov 22 2013

a(n) = 654*a(n-3) + a(n-6) for n>5. - Vincenzo Librandi, Dec 23 2013

Mathematica

Denominator[Convergents[Sqrt[370], 20]] (* Harvey P. Dale, Nov 01 2011 *)
CoefficientList[Series[-(x^4 - 4 x^3 + 17 x^2 + 4 x + 1)/(x^6 + 654 x^3 - 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 23 2013 *)

Prog

(Magma) I:=[1, 4, 17, 650, 2617, 11118]; [n le 6 select I[n] else 654*Self(n-3)+Self(n-6): n in [1..40]]; // Vincenzo Librandi, Dec 23 2013

Crossrefs

Cf. A041700, A040350.

Sequence in context: A153061 A277762 A337477 * A347721 A154131 A132554

Adjacent sequences: A041698 A041699 A041700 * A041702 A041703 A041704

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 22 2013

Status

approved