A041564 Numerators of continued fraction convergents to sqrt(300).

17, 52, 433, 1351, 46367, 140452, 1169983, 3650401, 125283617, 379501252, 3161293633, 9863382151, 338516286767, 1025412242452, 8541814226383, 26650854921601, 914670881560817, 2770663499604052, 23079978878393233, 72010600134783751, 2471440383461040767

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,2702,0,0,0,-1).

Formula

G.f.: -(x^7-17*x^6+52*x^5-433*x^4-1351*x^3-433*x^2-52*x-17) / ((x^4-52*x^2+1)*(x^4+52*x^2+1)). - Colin Barker, Nov 09 2013

a(n) = 2702*a(n-4) - a(n-8). - Wesley Ivan Hurt, Jan 20 2024

Mathematica

Numerator[Convergents[Sqrt[300], 30]] (* Vincenzo Librandi, Nov 04 2013 *)
LinearRecurrence[{0, 0, 0, 2702, 0, 0, 0, -1}, {17, 52, 433, 1351, 46367, 140452, 1169983, 3650401}, 30] (* Harvey P. Dale, May 20 2021 *)

Crossrefs

Cf. A041565.

Sequence in context: A041562 A113915 A042295 * A286211 A213997 A062342

Adjacent sequences: A041561 A041562 A041563 * A041565 A041566 A041567

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 09 2013

Status

approved