A042130 Numerators of continued fraction convergents to sqrt(590).

24, 73, 170, 753, 1676, 5781, 279164, 843273, 1965710, 8706113, 19377936, 66839921, 3227694144, 9749922353, 22727538850, 100660077753, 224047694356, 772803160821, 37318599413764, 112728601402113

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