A041501 Denominators of continued fraction convergents to sqrt(267).

1, 2, 3, 47, 50, 147, 4754, 9655, 14409, 225790, 240199, 706188, 22838215, 46382618, 69220833, 1084695113, 1153915946, 3392527005, 109714780106, 222822087217, 332536867323, 5210875097062, 5543411964385, 16297699025832, 527069780791009, 1070437260607850

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,4804,0,0,0,0,0,-1).

Formula

G.f.: -(x^10-2*x^9+3*x^8-47*x^7+50*x^6-147*x^5-50*x^4-47*x^3-3*x^2-2*x-1) / (x^12-4804*x^6+1). - Colin Barker, Nov 18 2013

a(n) = 4804*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 19 2013

Mathematica

Denominator[Convergents[Sqrt[267], 30]] (* Vincenzo Librandi, Dec 19 2013 *)

Prog

(Magma) I:=[1, 2, 3, 47, 50, 147, 4754, 9655, 14409, 225790, 240199, 706188]; [n le 12 select I[n] else 4804*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Dec 19 2013

Crossrefs

Cf. A041500, A040250.

Sequence in context: A171079 A097929 A266512 * A163488 A215536 A173355

Adjacent sequences: A041498 A041499 A041500 * A041502 A041503 A041504

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 18 2013

Status

approved