A041116 Numerators of continued fraction convergents to sqrt(67).

8, 41, 90, 131, 221, 1678, 1899, 3577, 9053, 48842, 790525, 4001467, 8793459, 12794926, 21588385, 163913621, 185502006, 349415627, 884333260, 4771081927, 77221644092, 390879302387, 858980248866, 1249859551253, 2108839800119, 16011738152086, 18120577952205

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,97684,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^19 -8*x^18 +41*x^17 -90*x^16 +131*x^15 -221*x^14 +1678*x^13 -1899*x^12 +3577*x^11 -9053*x^10 -48842*x^9 -9053*x^8 -3577*x^7 -1899*x^6 -1678*x^5 -221*x^4 -131*x^3 -90*x^2 -41*x -8) / (x^20 -97684*x^10 +1). - Colin Barker, Nov 10 2013

Mathematica

Numerator[Convergents[Sqrt[67], 30]] (* Vincenzo Librandi, Oct 29 2013 *)

Crossrefs

Cf. A010519, A041117.

Sequence in context: A209848 A093104 A120646 * A326286 A250322 A135797

Adjacent sequences: A041113 A041114 A041115 * A041117 A041118 A041119

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 10 2013

Status

approved