A042578 Numerators of continued fraction convergents to sqrt(818).

28, 29, 57, 86, 143, 8094, 8237, 16331, 24568, 40899, 2314912, 2355811, 4670723, 7026534, 11697257, 662072926, 673770183, 1335843109, 2009613292, 3345456401, 189355171748, 192700628149, 382055799897, 574756428046, 956812227943, 54156241192854

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, 286, 0, 0, 0, 0, 1).

Formula

G.f.: (28 +29*x +57*x^2 +86*x^3 +143*x^4 +86*x^5 -57*x^6 +29*x^7 -28*x^8 +x^9)/(1 -286*x^5 -x^10). - Bruno Berselli, Nov 28 2013

Mathematica

Numerator[Convergents[Sqrt[818], 30]] (* Vincenzo Librandi, Nov 28 2013 *)
CoefficientList[Series[(28 + 29 x + 57 x^2 + 86 x^3 + 143 x^4 + 86 x^5 - 57 x^6 + 29 x^7 - 28 x^8 + x^9)/(1 - 286 x^5 - x^10), {x, 0, 30}], x] (* Bruno Berselli, Nov 28 2013 *)
LinearRecurrence[{0, 0, 0, 0, 286, 0, 0, 0, 0, 1}, {28, 29, 57, 86, 143, 8094, 8237, 16331, 24568, 40899}, 30] (* Harvey P. Dale, Apr 05 2019 *)

Prog

(PARI) Vec((28+29*x+57*x^2+86*x^3+143*x^4+86*x^5-57*x^6+29*x^7-28*x^8+x^9)/(1-286*x^5-x^10)+O(x^99)) \\ Charles R Greathouse IV, Jun 12 2015

Crossrefs

Cf. A042579.

Sequence in context: A044874 A022398 A042580 * A042582 A042584 A042576

Adjacent sequences: A042575 A042576 A042577 * A042579 A042580 A042581

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved