A041208 Numerators of continued fraction convergents to sqrt(115).

10, 11, 32, 43, 75, 118, 193, 311, 815, 1126, 23335, 24461, 72257, 96718, 168975, 265693, 434668, 700361, 1835390, 2535751, 52550410, 55086161, 162722732, 217808893, 380531625, 598340518, 978872143, 1577212661, 4133297465, 5710510126, 118343499985

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,2252,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^19 -10*x^18 +11*x^17 -32*x^16 +43*x^15 -75*x^14 +118*x^13 -193*x^12 +311*x^11 -815*x^10 -1126*x^9 -815*x^8 -311*x^7 -193*x^6 -118*x^5 -75*x^4 -43*x^3 -32*x^2 -11*x -10) / (x^20 -2252*x^10 +1). - Colin Barker, Nov 05 2013

Mathematica

Numerator[Convergents[Sqrt[115], 30]] (* Vincenzo Librandi, Oct 31 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 2252, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {10, 11, 32, 43, 75, 118, 193, 311, 815, 1126, 23335, 24461, 72257, 96718, 168975, 265693, 434668, 700361, 1835390, 2535751}, 40] (* Harvey P. Dale, Feb 12 2026 *)

Crossrefs

Cf. A041209.

Sequence in context: A098795 A108580 A356279 * A041485 A041206 A376219

Adjacent sequences: A041205 A041206 A041207 * A041209 A041210 A041211

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Colin Barker, Nov 05 2013

Status

approved