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

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

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).

Crossrefs

Cf. A010522, A041123.

Programs

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 *)

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]