A041808 Numerators of continued fraction convergents to sqrt(425).

20, 21, 41, 62, 103, 165, 268, 10885, 11153, 22038, 33191, 55229, 88420, 143649, 5834380, 5978029, 11812409, 17790438, 29602847, 47393285, 76996132, 3127238565, 3204234697, 6331473262, 9535707959, 15867181221, 25402889180, 41270070401, 1676205705220

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, 536, 0, 0, 0, 0, 0, 0, 1).

Formula

G.f.: -(x^13 -20*x^12 +21*x^11 -41*x^10 +62*x^9 -103*x^8 +165*x^7 +268*x^6 +165*x^5 +103*x^4 +62*x^3 +41*x^2 +21*x +20) / (x^14 +536*x^7 -1). - Colin Barker, Nov 25 2013

Mathematica

Numerator[Convergents[Sqrt[425], 30]] (* Vincenzo Librandi, Nov 09 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 536, 0, 0, 0, 0, 0, 0, 1}, {20, 21, 41, 62, 103, 165, 268, 10885, 11153, 22038, 33191, 55229, 88420, 143649}, 40] (* Harvey P. Dale, Dec 10 2022 *)

Crossrefs

Cf. A041809, A040404.

Sequence in context: A075034 A363770 A022110 * A041810 A042855 A041812

Adjacent sequences: A041805 A041806 A041807 * A041809 A041810 A041811

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 25 2013

Status

approved