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A042130 Numerators of continued fraction convergents to sqrt(590). 2
24, 73, 170, 753, 1676, 5781, 279164, 843273, 1965710, 8706113, 19377936, 66839921, 3227694144, 9749922353, 22727538850, 100660077753, 224047694356, 772803160821, 37318599413764, 112728601402113 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,11562,0,0,0,0,0,-1).

FORMULA

G.f.: -(x^11 - 24*x^10 + 73*x^9 - 170*x^8 + 753*x^7 - 1676*x^6 - 5781*x^5 - 1676*x^4 - 753*x^3 - 170*x^2 - 73*x - 24)/(x^12 - 11562*x^6 + 1). [Vincenzo Librandi, Nov 17 2013]

a(n) = 11562*a(n-6) - a(n-12). - Vincenzo Librandi, Nov 17 2013

MATHEMATICA

Numerator[Convergents[Sqrt[590], 30]] (* or *) CoefficientList[Series[-(x^11 - 24 x^10 + 73 x^9 - 170 x^8 + 753 x^7 - 1676 x^6 - 5781 x^5 - 1676 x^4 - 753 x^3 - 170 x^2 - 73 x - 24)/(x^12 - 11562 x^6 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 17 2013 *)

PROG

(MAGMA) I:=[24, 73, 170, 753, 1676, 5781, 279164, 843273, 1965710, 8706113, 19377936, 66839921]; [n le 12 select I[n] else 11562*Self(n-6)-Self(n-12): n in [1..25]]; // Vincenzo Librandi, Nov 17 2013

CROSSREFS

Cf. A042131.

Sequence in context: A044162 A044543 A161587 * A042132 A042134 A045249

Adjacent sequences:  A042127 A042128 A042129 * A042131 A042132 A042133

KEYWORD

nonn,cofr,frac,easy,less

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified May 23 10:05 EDT 2022. Contains 353975 sequences. (Running on oeis4.)