A041157 Denominators of continued fraction convergents to sqrt(88).
1, 2, 3, 5, 8, 21, 386, 793, 1179, 1972, 3151, 8274, 152083, 312440, 464523, 776963, 1241486, 3259935, 59920316, 123100567, 183020883, 306121450, 489142333, 1284406116, 23608452421, 48501310958, 72109763379, 120611074337, 192720837716, 506052749769
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,394,0,0,0,0,0,-1).
Programs
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Mathematica
Denominator/@Convergents[Sqrt[88], 50] (* Vladimir Joseph Stephan Orlovsky, Jul 05 2011 *) CoefficientList[Series[- (x^10 - 2 x^9 + 3 x^8 - 5 x^7 + 8 x^6 - 21 x^5 - 8 x^4 - 5 x^3 - 3 x^2 - 2 x - 1)/(x^12 - 394 x^6 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 24 2013 *) LinearRecurrence[{0,0,0,0,0,394,0,0,0,0,0,-1},{1,2,3,5,8,21,386,793,1179,1972,3151,8274},30] (* Harvey P. Dale, Jul 28 2017 *)
Formula
a(n) = 394*a(n-6)-a(n-12). G.f.: -(x^10-2*x^9+3*x^8-5*x^7+8*x^6 -21*x^5 -8*x^4 -5*x^3-3*x^2-2*x-1) / (x^12-394*x^6+1). - Colin Barker, Jul 18 2012