A041206 Numerators of continued fraction convergents to sqrt(114).

10, 11, 32, 331, 694, 1025, 21194, 22219, 65632, 678539, 1422710, 2101249, 43447690, 45548939, 134545568, 1391004619, 2916554806, 4307559425, 89067743306, 93375302731, 275818348768, 2851558790411

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,2050,0,0,0,0,0,-1).

Formula

a(n) = 2050*a(n-6)-a(n-12). G.f.: -(x^11-10*x^10+11*x^9-32*x^8+331*x^7-694*x^6-1025*x^5-694*x^4-331*x^3-32*x^2-11*x-10)/(x^12-2050*x^6+1). [Colin Barker, Jul 19 2012]

Mathematica

Numerator[Convergents[Sqrt[114], 30]] (* Vincenzo Librandi, Oct 26 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 2050, 0, 0, 0, 0, 0, -1}, {10, 11, 32, 331, 694, 1025, 21194, 22219, 65632, 678539, 1422710, 2101249}, 30] (* Harvey P. Dale, Nov 30 2024 *)

Crossrefs

Cf. A041207.

Sequence in context: A356279 A041208 A041485 * A376219 A339078 A097990

Adjacent sequences: A041203 A041204 A041205 * A041207 A041208 A041209

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved