A041200 Numerators of continued fraction convergents to sqrt(111).

10, 11, 21, 137, 158, 295, 6058, 6353, 12411, 80819, 93230, 174049, 3574210, 3748259, 7322469, 47683073, 55005542, 102688615, 2108777842, 2211466457, 4320244299, 28132932251, 32453176550, 60586108801

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,590,0,0,0,0,0,-1).

Formula

a(n) = 590*a(n-6)-a(n-12). G.f.: -(x^11-10*x^10+11*x^9-21*x^8+137*x^7-158*x^6-295*x^5-158*x^4-137*x^3-21*x^2-11*x-10)/(x^12-590*x^6+1). [Colin Barker, Jul 19 2012]

Mathematica

Numerator[Convergents[Sqrt[111], 30]] (* Vincenzo Librandi, Oct 26 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 590, 0, 0, 0, 0, 0, -1}, {10, 11, 21, 137, 158, 295, 6058, 6353, 12411, 80819, 93230, 174049}, 30] (* Harvey P. Dale, Jul 07 2024 *)

Crossrefs

Cf. A041201.

Sequence in context: A041202 A324550 A214617 * A041847 A113702 A373616

Adjacent sequences: A041197 A041198 A041199 * A041201 A041202 A041203

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved