A041054 Numerators of continued fraction convergents to sqrt(33).

5, 6, 17, 23, 247, 270, 787, 1057, 11357, 12414, 36185, 48599, 522175, 570774, 1663723, 2234497, 24008693, 26243190, 76495073, 102738263, 1103877703, 1206615966, 3517109635, 4723725601, 50754365645

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,46,0,0,0,-1).

Crossrefs

Cf. A010488, A041055.

Programs

Mathematica

Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[33], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 18 2011 *)
Numerator[Convergents[Sqrt[33],30]] (* Harvey P. Dale, Oct 25 2011 *)
CoefficientList[Series[- (x^7 - 5 x^6 + 6 x^5 - 17 x^4 - 23 x^3 - 17 x^2 - 6 x - 5)/(x^8 - 46 x^4 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 23 2013 *)

Formula

a(n) = 46*a(n-4)-a(n-8). G.f.: -(x^7-5*x^6+6*x^5-17*x^4-23*x^3-17*x^2-6*x-5)/(x^8-46*x^4+1). [Colin Barker, Jul 16 2012]