A042900 Numerators of continued fraction convergents to sqrt(982).

31, 63, 94, 2883, 2977, 8837, 550871, 1110579, 1661450, 50954079, 52615529, 156185137, 9736094023, 19628373183, 29364467206, 900562389363, 929926856569, 2760416102501, 172075725211631, 346911866525763, 518987591737394, 15916539618647583, 16435527210384977

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, 17674, 0, 0, 0, 0, 0, -1).

Formula

G.f.: (31 + 63*x + 94*x^2 + 2883*x^3 + 2977*x^4 + 8837*x^5 + 2977*x^6 - 2883*x^7 + 94*x^8 - 63*x^9 + 31*x^10 - x^11)/(1 - 17674*x^6 + x^12). - Vincenzo Librandi, Dec 09 2013

a(n) = 17674*a(n-6) - a(n-12). - Vincenzo Librandi, Dec 09 2013

Mathematica

Numerator[Convergents[Sqrt[982], 30]] (* or *) CoefficientList[Series[(31 + 63 x + 94 x^2 + 2883 x^3 + 2977 x^4 + 8837 x^5 + 2977 x^6 - 2883 x^7 + 94 x^8 - 63 x^9 + 31 x^10 - x^11)/(1 - 17674 x^6 + x^12), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 09 2013 *)

Prog

(Magma) I:=[31, 63, 94, 2883, 2977, 8837, 550871, 1110579, 1661450, 50954079, 52615529, 156185137]; [n le 12 select I[n] else 17674*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Dec 09 2013

Crossrefs

Cf. A042901.

Sequence in context: A042906 A042904 A042902 * A239128 A042910 A042908

Adjacent sequences: A042897 A042898 A042899 * A042901 A042902 A042903

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Dec 09 2013

Status

approved