A042538 Numerators of continued fraction convergents to sqrt(798).

28, 113, 6356, 25537, 1436428, 5771249, 324626372, 1304276737, 73364123644, 294760771313, 16579967317172, 66614630040001, 3746999249557228, 15054611628268913, 846805250432616356

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,226,0,-1).

Formula

G.f.: (28 + 113*x + 28*x^2 - x^3)/(1 - 226*x^2 + x^4). - Vincenzo Librandi, Nov 27 2013

a(n) = 226*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 27 2013

Mathematica

Numerator[Convergents[Sqrt[798], 30]] (* or *) CoefficientList[Series[(28 + 113 x + 28 x^2 - x^3)/(1 - 226 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 27 2013 *)
LinearRecurrence[{0, 226, 0, -1}, {28, 113, 6356, 25537}, 20] (* Harvey P. Dale, Mar 14 2023 *)

Prog

(Magma) I:=[28, 113, 6356, 25537]; [n le 4 select I[n] else 226*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 27 2013

Crossrefs

Cf. A042539.

Sequence in context: A219594 A042534 A042536 * A251320 A233372 A220755

Adjacent sequences: A042535 A042536 A042537 * A042539 A042540 A042541

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Status

approved