A042784 Numerators of continued fraction convergents to sqrt(923).

30, 61, 91, 152, 243, 638, 38523, 77684, 116207, 193891, 310098, 814087, 49155318, 99124723, 148280041, 247404764, 395684805, 1038774374, 62722147245, 126483068864, 189205216109, 315688284973, 504893501082, 1325475287137, 80033410729302

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, 1276, 0, 0, 0, 0, 0, -1).

Formula

G.f.: (30 +61*x +91*x^2 +152*x^3 +243*x^4 +638*x^5 +243*x^6 -152*x^7 +91*x^8 -61*x^9 +30*x^10 -x^11)/(1 -1276*x^6 +x^12). - Vincenzo Librandi, Dec 04 2013

a(n) = 1276*a(n-6) - a(n-12). - Vincenzo Librandi, Dec 04 2013

Mathematica

Numerator[Convergents[Sqrt[923], 30]] (* or *) CoefficientList[Series[(30 + 61 x + 91 x^2 + 152 x^3 + 243 x^4 + 638 x^5 + 243 x^6 - 152 x^7 + 91 x^8 - 61 x^9 + 30 x^10 - x^11)/(1 - 1276 x^6 + x^12), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 04 2013 *)

Prog

(Magma) I:=[30, 61, 91, 152, 243, 638, 38523, 77684, 116207, 193891, 310098, 814087]; [n le 12 select I[n] else 1276*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Dec 04 2013

Crossrefs

Cf. A042785.

Sequence in context: A228877 A258879 A053014 * A042786 A042782 A042780

Adjacent sequences: A042781 A042782 A042783 * A042785 A042786 A042787

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Dec 04 2013

Status

approved