A041531 Denominators of continued fraction convergents to sqrt(282).

1, 1, 4, 5, 24, 29, 111, 140, 4591, 4731, 18784, 23515, 112844, 136359, 521921, 658280, 21586881, 22245161, 88322364, 110567525, 530592464, 641159989, 2454072431, 3095232420, 101501509871, 104596742291, 415291736744, 519888479035, 2494845652884

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, 4702, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^2-x-1)*(x^4+5*x^2+1)*(x^8+28*x^4+1) / (x^16-4702*x^8+1). - Colin Barker, Nov 18 2013

a(n) = 4702*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Dec 19 2013

Mathematica

Denominator[Convergents[Sqrt[282], 30]] (* Vincenzo Librandi, Dec 19 2013 *)

Prog

(Magma) I:=[1, 1, 4, 5, 24, 29, 111, 140, 4591, 4731, 18784, 23515, 112844, 136359, 521921, 658280]; [n le 16 select I[n] else 4702*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 19 2013

Crossrefs

Cf. A041530, A040265.

Sequence in context: A063986 A039583 A042123 * A089499 A249060 A042601

Adjacent sequences: A041528 A041529 A041530 * A041532 A041533 A041534

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 18 2013

Status

approved