A042248 Numerators of continued fraction convergents to sqrt(650).

25, 51, 2575, 5201, 262625, 530451, 26785175, 54100801, 2731825225, 5517751251, 278619387775, 562756526801, 28416445727825, 57395647982451, 2898198844850375, 5853793337683201, 295587865729010425, 597029524795704051

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,102,0,-1).

Formula

G.f.: (1 + x)*(25 + 26*x - x^2)/((1 - 10*x - x^2)*(1 + 10*x - x^2)) = (25 + 51*x + 25*x^2 - x^3)/(1 - 102*x^2 + x^4). - Vincenzo Librandi, Nov 20 2013

a(n) = 102*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 20 2013

Mathematica

Numerator[Convergents[Sqrt[650], 30]] (* or *) CoefficientList[Series[(25 + 51 x + 25 x^2 - x^3)/(1 - 102 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 20 2013 *)

Prog

(Magma) I:=[25, 51, 2575, 5201]; [n le 4 select I[n] else 102*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 20 2013

Crossrefs

Cf. A042249.

Sequence in context: A042242 A042244 A042246 * A132766 A039412 A352260

Adjacent sequences: A042245 A042246 A042247 * A042249 A042250 A042251

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved