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A041345 Denominators of continued fraction convergents to sqrt(186). 2
1, 1, 2, 3, 11, 47, 152, 199, 351, 550, 14651, 15201, 29852, 45053, 165011, 705097, 2280302, 2985399, 5265701, 8251100, 219794301, 228045401, 447839702, 675885103, 2475495011, 10577865147, 34209090452, 44786955599, 78996046051, 123783001650 (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 (0,0,0,0,0,0,0,0,0,15002,0,0,0,0,0,0,0,0,0,-1).

FORMULA

G.f.: -(x^18 -x^17 +2*x^16 -3*x^15 +11*x^14 -47*x^13 +152*x^12 -199*x^11 +351*x^10 -550*x^9 -351*x^8 -199*x^7 -152*x^6 -47*x^5 -11*x^4 -3*x^3 -2*x^2 -x -1) / (x^20 -15002*x^10 +1). - Colin Barker, Nov 15 2013

a(n) = 15002*a(n-10) - a(n-20). - Vincenzo Librandi, Dec 16 2013

MATHEMATICA

Denominator[Convergents[Sqrt[186], 30]] (* Vincenzo Librandi, Dec 16 2013 *)

PROG

(MAGMA) I:=[1, 1, 2, 3, 11, 47, 152, 199, 351, 550, 14651, 15201, 29852, 45053, 165011, 705097, 2280302, 2985399, 5265701, 8251100]; [n le 20 select I[n] else 15002*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 16 2013

CROSSREFS

Cf. A041344, A010228.

Sequence in context: A128455 A260159 A287060 * A268285 A100701 A011365

Adjacent sequences:  A041342 A041343 A041344 * A041346 A041347 A041348

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Colin Barker, Nov 15 2013

STATUS

approved

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Last modified February 22 15:05 EST 2020. Contains 332137 sequences. (Running on oeis4.)