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
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).
Programs
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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]