A042132 Numerators of continued fraction convergents to sqrt(591).

24, 73, 316, 389, 705, 5324, 6029, 11353, 51441, 165676, 8003889, 24177343, 104713261, 128890604, 233603865, 1764117659, 1997721524, 3761839183, 17045078256, 54897073951, 2652104627904, 8011210957663, 34696948458556, 42708159416219, 77405107874775

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,331352,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: (24 +73*x +316*x^2 +389*x^3 +705*x^4 +5324*x^5 +6029*x^6 +11353*x^7 +51441*x^8 +165676*x^9 +51441*x^10 -11353*x^11 +6029*x^12 -5324*x^13 +705*x^14 -389*x^15 +316*x^16 -73*x^17 +24*x^18 -x^19)/(1 -331352*x^10 +x^20). [Bruno Berselli, Nov 17 2013]

a(n) = 331352*a(n-10) - a(n-20) for n>19. [Bruno Berselli, Nov 17 2013]

Mathematica

Numerator[Convergents[Sqrt[591], 30]] (* Vincenzo Librandi, Nov 17 2013 *)
CoefficientList[Series[(24 + 73 x + 316 x^2 + 389 x^3 + 705 x^4 + 5324 x^5 + 6029 x^6 + 11353 x^7 + 51441 x^8 + 165676 x^9 + 51441 x^10 - 11353 x^11 + 6029 x^12 - 5324 x^13 + 705 x^14 - 389 x^15 + 316 x^16 - 73 x^17 + 24 x^18 - x^19)/(1 - 331352 x^10 + x^20), {x, 0, 30}], x] (* Bruno Berselli, Nov 17 2013 *)

Crossrefs

Cf. A042133.

Sequence in context: A044543 A161587 A042130 * A042134 A045249 A185940

Adjacent sequences: A042129 A042130 A042131 * A042133 A042134 A042135

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane

Status

approved