A042066 Numerators of continued fraction convergents to sqrt(557).

23, 24, 47, 71, 118, 5499, 5617, 11116, 16733, 27849, 1297787, 1325636, 2623423, 3949059, 6572482, 306283231, 312855713, 619138944, 931994657, 1551133601, 72284140303, 73835273904, 146119414207, 219954688111, 366074102318, 17059363394739, 17425437497057

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, 236, 0, 0, 0, 0, 1).

Formula

G.f.: (23 +24*x +47*x^2 +71*x^3 +118*x^4 +71*x^5 -47*x^6 +24*x^7 -23*x^8 +x^9)/(1 -236*x^5 -x^10). [Bruno Berselli, Nov 15 2013]

Mathematica

Numerator[Convergents[Sqrt[557], 30]] (* Vincenzo Librandi, Nov 14 2013 *)
CoefficientList[Series[(23 + 24 x + 47 x^2 + 71 x^3 + 118 x^4 + 71 x^5 - 47 x^6 + 24 x^7 - 23 x^8 + x^9)/(1 - 236 x^5 - x^10), {x, 0, 30}], x] (* Bruno Berselli, Nov 15 2013 *)

Crossrefs

Cf. A042067.

Sequence in context: A122470 A022393 A042068 * A042070 A042072 A042064

Adjacent sequences: A042063 A042064 A042065 * A042067 A042068 A042069

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved