A042688 Numerators of continued fraction convergents to sqrt(874).

29, 30, 59, 207, 473, 1626, 2099, 3725, 218149, 221874, 440023, 1541943, 3523909, 12113670, 15637579, 27751249, 1625210021, 1652961270, 3278171291, 11487475143, 26253121577, 90246839874, 116499961451, 206746801325, 12107814438301, 12314561239626

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, 0, 0, 0, 7450, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^15 -29*x^14 +30*x^13 -59*x^12 +207*x^11 -473*x^10 +1626*x^9 -2099*x^8 -3725*x^7 -2099*x^6 -1626*x^5 -473*x^4 -207*x^3 -59*x^2 -30*x -29) / (x^16 -7450*x^8 +1). - Colin Barker, Dec 21 2013

Mathematica

Numerator[Convergents[Sqrt[874], 30]] (* Vincenzo Librandi, Dec 01 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 7450, 0, 0, 0, 0, 0, 0, 0, -1}, {29, 30, 59, 207, 473, 1626, 2099, 3725, 218149, 221874, 440023, 1541943, 3523909, 12113670, 15637579, 27751249}, 30] (* Harvey P. Dale, Dec 11 2014 *)

Crossrefs

Cf. A042689, A040844.

Sequence in context: A042700 A042690 A042692 * A042686 A042684 A042682

Adjacent sequences: A042685 A042686 A042687 * A042689 A042690 A042691

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 21 2013

Status

approved