A041869 Denominators of continued fraction convergents to sqrt(456).

1, 2, 3, 14, 17, 48, 2033, 4114, 6147, 28702, 34849, 98400, 4167649, 8433698, 12601347, 58839086, 71440433, 201719952, 8543678417, 17289076786, 25832755203, 120620097598, 146452852801, 413525803200, 17514536587201, 35442598977602, 52957135564803

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,2050,0,0,0,0,0,-1).

Formula

G.f.: -(x^10 -2*x^9 +3*x^8 -14*x^7 +17*x^6 -48*x^5 -17*x^4 -14*x^3 -3*x^2 -2*x-1) / (x^12 -2050*x^6 +1). - Colin Barker, Nov 26 2013

a(n) = 2050*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 26 2013

Mathematica

Denominator[Convergents[Sqrt[456], 30]] (* Vincenzo Librandi, Dec 26 2013 *)

Prog

(Magma) I:=[1, 2, 3, 14, 17, 48, 2033, 4114, 6147, 28702, 34849, 98400]; [n le 12 select I[n] else 2050*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 26 2013

Crossrefs

Cf. A041868, A040434.

Sequence in context: A041009 A042367 A100341 * A041010 A041733 A212112

Adjacent sequences: A041866 A041867 A041868 * A041870 A041871 A041872

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 26 2013

Status

approved