A041873 Denominators of continued fraction convergents to sqrt(458).

1, 2, 5, 212, 429, 1070, 45369, 91808, 228985, 9709178, 19647341, 49003860, 2077809461, 4204622782, 10487055025, 444660933832, 899808922689, 2244278779210, 95159517649509, 192563314078228, 480286145805965, 20364581437928758, 41209449021663481

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,214,0,0,1).

Formula

G.f.: -(x^4 -2*x^3 +5*x^2 +2*x +1) / (x^6 +214*x^3 -1). - Colin Barker, Nov 26 2013

a(n) = 214*a(n-3) + a(n-6) for n>5. - Vincenzo Librandi, Dec 26 2013

Mathematica

Denominator[Convergents[Sqrt[458], 30]] (* Vincenzo Librandi, Dec 26 2013 *)

Prog

(Magma) I:=[1, 2, 5, 212, 429, 1070]; [n le 6 select I[n] else 214*Self(n-3)+Self(n-6): n in [1..40]]; // Vincenzo Librandi, Dec 26 2013

Crossrefs

Cf. A041872, A040436.

Sequence in context: A027682 A096695 A084297 * A072118 A249180 A135724

Adjacent sequences: A041870 A041871 A041872 * A041874 A041875 A041876

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 26 2013

Status

approved