A041130 Numerators of continued fraction convergents to sqrt(74).

8, 9, 17, 26, 43, 714, 757, 1471, 2228, 3699, 61412, 65111, 126523, 191634, 318157, 5282146, 5600303, 10882449, 16482752, 27365201, 454325968, 481691169, 936017137, 1417708306, 2353725443, 39077315394, 41431040837, 80508356231, 121939397068, 202447753299

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,86,0,0,0,0,1).

Formula

G.f.: -(x^9-8*x^8+9*x^7-17*x^6+26*x^5+43*x^4+26*x^3+17*x^2+9*x+8) / (x^10+86*x^5-1). - Colin Barker, Nov 05 2013

Mathematica

Numerator[Convergents[Sqrt[74], 30]] (* Vincenzo Librandi, Oct 29 2013 *)
LinearRecurrence[{0, 0, 0, 0, 86, 0, 0, 0, 0, 1}, {8, 9, 17, 26, 43, 714, 757, 1471, 2228, 3699}, 40] (* Harvey P. Dale, Sep 18 2024 *)

Crossrefs

Cf. A010526, A041131.

Sequence in context: A261454 A022098 A129659 * A041307 A042289 A041132

Adjacent sequences: A041127 A041128 A041129 * A041131 A041132 A041133

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Colin Barker, Nov 05 2013

Status

approved