A041122 Numerators of continued fraction convergents to sqrt(70).

8, 17, 25, 67, 92, 251, 4108, 8467, 12575, 33617, 46192, 126001, 2062208, 4250417, 6312625, 16875667, 23188292, 63252251, 1035224308, 2133700867, 3168925175, 8471551217, 11640476392, 31752504001

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,502,0,0,0,0,0,-1).

Formula

a(n) = 502*a(n-6)-a(n-12). G.f.: -(x+1)*(x^10-9*x^9+26*x^8-51*x^7+118*x^6-210*x^5-41*x^4-51*x^3-16*x^2-9*x-8)/(x^12-502*x^6+1). [Colin Barker, Jul 18 2012]

Mathematica

Numerator[Convergents[Sqrt[70], 30]] (* Vincenzo Librandi, Oct 26 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 502, 0, 0, 0, 0, 0, -1}, {8, 17, 25, 67, 92, 251, 4108, 8467, 12575, 33617, 46192, 126001}, 30] (* Harvey P. Dale, Dec 12 2024 *)

Crossrefs

Cf. A010522, A041123.

Sequence in context: A046464 A022390 A041831 * A042211 A290227 A277052

Adjacent sequences: A041119 A041120 A041121 * A041123 A041124 A041125

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved