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%I #20 Jun 13 2015 00:49:22
%S 9,37,46,83,378,6887,27926,34813,62739,285769,5206581,21112093,
%T 26318674,47430767,216041742,3936182123,15960770234,19896952357,
%U 35857722591,163327842721,2975758891569,12066363408997
%N Numerators of continued fraction convergents to sqrt(85).
%C From _Johannes W. Meijer_, Jun 17 2010: (Start)
%C The a(n) terms of this sequence can be constructed with the terms of sequence A087798.
%C For the terms of the periodic sequence of the continued fraction for sqrt(85) see A010158. We observe that its period is five. The decimal expansion of sqrt(85) is A010536. (End)
%H Vincenzo Librandi, <a href="/A041150/b041150.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,756,0,0,0,0,1).
%F From _Johannes W. Meijer_, Jun 17 2010: (Start)
%F a(5*n) = A087798(3*n+1), a(5*n+1) = (A087798(3*n+2) - A087798(3*n+1))/2, a(5*n+2) = (A087798(3*n+2) + A087798(3*n+1))/2, a(5*n+3) = A087798(3*n+2) and a(5*n+4) = A087798(3*n+3)/2. (End)
%F G.f.: -(x^9-9*x^8+37*x^7-46*x^6+83*x^5+378*x^4+83*x^3+46*x^2+37*x+9) / (x^10+756*x^5-1). - _Colin Barker_, Nov 04 2013
%t Numerator[Convergents[Sqrt[85], 30]] (* _Vincenzo Librandi_, Oct 29 2013 *)
%Y Cf. A010536, A041018, A041046, A041090, A041150, A041151, A041226, A041318, A041426,
%Y A041550.
%K nonn,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
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