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A041247 Denominators of continued fraction convergents to sqrt(135). 2
1, 1, 2, 3, 5, 8, 13, 21, 475, 496, 971, 1467, 2438, 3905, 6343, 10248, 231799, 242047, 473846, 715893, 1189739, 1905632, 3095371, 5001003, 113117437, 118118440, 231235877, 349354317, 580590194, 929944511, 1510534705, 2440479216, 55201077457, 57641556673 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,488,0,0,0,0,0,0,0,-1).

FORMULA

G.f.: -(x^2-x-1)*(x^4+3*x^2+1)*(x^8+7*x^4+1) / (x^16-488*x^8+1). - Colin Barker, Nov 14 2013

a(n) = 488*a(n-8) - a(n-16). - Vincenzo Librandi, Dec 13 2013

MATHEMATICA

Denominator[Convergents[Sqrt[135], 30]]  (* Vincenzo Librandi, Dec 13 2013 *)

LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 488, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 1, 2, 3, 5, 8, 13, 21, 475, 496, 971, 1467, 2438, 3905, 6343, 10248}, 40] (* Harvey P. Dale, Aug 01 2019 *)

PROG

(MAGMA) I:=[1, 1, 2, 3, 5, 8, 13, 21, 475, 496, 971, 1467, 2438, 3905, 6343, 10248]; [n le 16 select I[n] else 488*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 13 2013

CROSSREFS

Cf. A041246, A010194.

Sequence in context: A067517 A042339 A137574 * A117770 A053412 A198202

Adjacent sequences:  A041244 A041245 A041246 * A041248 A041249 A041250

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Colin Barker, Nov 14 2013

STATUS

approved

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Last modified November 22 16:26 EST 2019. Contains 329396 sequences. (Running on oeis4.)