A042072 Numerators of continued fraction convergents to sqrt(560).

23, 24, 47, 71, 3313, 3384, 6697, 10081, 470423, 480504, 950927, 1431431, 66796753, 68228184, 135024937, 203253121, 9484668503, 9687921624, 19172590127, 28860511751, 1346756130673, 1375616642424, 2722372773097, 4097989415521, 191229885887063

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,142,0,0,0,-1).

Formula

G.f.: (23 +24*x +47*x^2 +71*x^3 +47*x^4 -24*x^5 +23*x^6 -x^7)/((1 -12x^2 +x^4)*(1 +12*x^2 +x^4)). [Bruno Berselli, Nov 15 2013]

Mathematica

Numerator[Convergents[Sqrt[560], 30]] (* Vincenzo Librandi, Nov 15 2013 *)
CoefficientList[Series[(23 + 24 x + 47 x^2 + 71 x^3 + 47 x^4 - 24 x^5 + 23 x^6 - x^7)/(1 - 142 x^4 + x^8), {x, 0, 30}], x] (* Bruno Berselli, Nov 15 2013 *)
LinearRecurrence[{0, 0, 0, 142, 0, 0, 0, -1}, {23, 24, 47, 71, 3313, 3384, 6697, 10081}, 30] (* Harvey P. Dale, Aug 11 2019 *)

Crossrefs

Cf. A042073.

Sequence in context: A042068 A042066 A042070 * A042064 A042062 A042060

Adjacent sequences: A042069 A042070 A042071 * A042073 A042074 A042075

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Status

approved