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Numerators of continued fraction convergents to sqrt(53).
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%I #24 Jun 13 2015 00:49:21

%S 7,22,29,51,182,2599,7979,10578,18557,66249,946043,2904378,3850421,

%T 6754799,24114818,344362251,1057201571,1401563822,2458765393,

%U 8777860001,125348805407,384824276222,510173081629,894997357851,3195165155182,45627309530399

%N Numerators of continued fraction convergents to sqrt(53).

%C The terms of this sequence can be constructed with the terms of sequence A086902. For the terms of the periodical sequence of the continued fraction for sqrt(53) see A010139. We observe that its period is five. The decimal expansion of sqrt(53) is A010506. - _Johannes W. Meijer_, Jun 12 2010

%H Vincenzo Librandi, <a href="/A041090/b041090.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,364,0,0,0,0,1).

%F a(5*n) = A086902(3*n+1), a(5*n+1) = (A086902(3*n+2)-A086902(3*n+1))/2, a(5*n+2) = (A086902(3*n+2)+A086902(3*n+1))/2, a(5*n+3) = A086902(3*n+2) and a(5*n+4) = A086902(3*n+3)/2. - _Johannes W. Meijer_, Jun 12 2010

%F G.f.: -(x^9-7*x^8+22*x^7-29*x^6+51*x^5+182*x^4+51*x^3+29*x^2+22*x+7) / (x^10+364*x^5-1). - _Colin Barker_, Sep 26 2013

%t Numerator[Convergents[Sqrt[53],30]] (* _Harvey P. Dale_, Sep 24 2013 *)

%t CoefficientList[Series[-(x^9 - 7 x^8 + 22 x^7 - 29 x^6 + 51 x^5 + 182 x^4 + 51 x^3 + 29 x^2 + 22 x + 7)/(x^10 + 364 x^5 - 1), {x, 0, 40}], x] (* _Vincenzo Librandi_, Sep 27 2013 *)

%Y Cf. A041091, A041018, A041046, A041150, A041226, A041318, A041426 and A041550.

%K nonn,frac,easy

%O 0,1

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Sep 26 2013