A041234 Numerators of continued fraction convergents to sqrt(129).

11, 23, 34, 125, 159, 1079, 1238, 4793, 6031, 16855, 376841, 770537, 1147378, 4212671, 5360049, 36372965, 41733014, 161572007, 203305021, 568182049, 12703310099, 25974802247, 38678112346, 142009139285, 180687251631, 1226132649071, 1406819900702

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,33710,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^19 -11*x^18 +23*x^17 -34*x^16 +125*x^15 -159*x^14 +1079*x^13 -1238*x^12 +4793*x^11 -6031*x^10 -16855*x^9 -6031*x^8 -4793*x^7 -1238*x^6 -1079*x^5 -159*x^4 -125*x^3 -34*x^2 -23*x -11) / (x^20 -33710*x^10 +1). - Colin Barker, Nov 10 2013

Mathematica

Numerator[Convergents[Sqrt[129], 30]] (* Vincenzo Librandi, Oct 31 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 33710, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {11, 23, 34, 125, 159, 1079, 1238, 4793, 6031, 16855, 376841, 770537, 1147378, 4212671, 5360049, 36372965, 41733014, 161572007, 203305021, 568182049}, 30] (* Harvey P. Dale, Feb 06 2023 *)

Crossrefs

Cf. A041235.

Sequence in context: A250215 A208326 A097657 * A041549 A136771 A017653

Adjacent sequences: A041231 A041232 A041233 * A041235 A041236 A041237

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 10 2013

Status

approved