A041651 Denominators of continued fraction convergents to sqrt(344).

1, 1, 2, 9, 11, 42, 53, 254, 307, 561, 20503, 21064, 41567, 187332, 228899, 874029, 1102928, 5285741, 6388669, 11674410, 426667429, 438341839, 865009268, 3898378911, 4763388179, 18188543448, 22951931627, 109996269956, 132948201583, 242944471539

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, 20810, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^18 -x^17 +2*x^16 -9*x^15 +11*x^14 -42*x^13 +53*x^12 -254*x^11 +307*x^10 -561*x^9 -307*x^8 -254*x^7 -53*x^6 -42*x^5 -11*x^4 -9*x^3 -2*x^2 -x -1) / (x^20 -20810*x^10 +1). - Colin Barker, Nov 20 2013

a(n) = 20810*a(n-10) - a(n-20) for n>19. - Vincenzo Librandi, Dec 22 2013

Mathematica

Denominator[Convergents[Sqrt[344], 30]] (* Vincenzo Librandi, Dec 22 2013 *)

Prog

(Magma) I:=[1, 1, 2, 9, 11, 42, 53, 254, 307, 561, 20503, 21064, 41567, 187332, 228899, 874029, 1102928, 5285741, 6388669, 11674410]; [n le 20 select I[n] else 20810*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 22 2013

Crossrefs

Cf. A041650, A040325.

Sequence in context: A042053 A134775 A042573 * A042687 A083159 A041335

Adjacent sequences: A041648 A041649 A041650 * A041652 A041653 A041654

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 20 2013

Status

approved