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%I #17 Jun 13 2015 00:49:39
%S 24,73,316,389,705,5324,6029,11353,51441,165676,8003889,24177343,
%T 104713261,128890604,233603865,1764117659,1997721524,3761839183,
%U 17045078256,54897073951,2652104627904,8011210957663,34696948458556,42708159416219,77405107874775
%N Numerators of continued fraction convergents to sqrt(591).
%H Vincenzo Librandi, <a href="/A042132/b042132.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 (0,0,0,0,0,0,0,0,0,331352,0,0,0,0,0,0,0,0,0,-1).
%F G.f.: (24 +73*x +316*x^2 +389*x^3 +705*x^4 +5324*x^5 +6029*x^6 +11353*x^7 +51441*x^8 +165676*x^9 +51441*x^10 -11353*x^11 +6029*x^12 -5324*x^13 +705*x^14 -389*x^15 +316*x^16 -73*x^17 +24*x^18 -x^19)/(1 -331352*x^10 +x^20). [_Bruno Berselli_, Nov 17 2013]
%F a(n) = 331352*a(n-10) - a(n-20) for n>19. [_Bruno Berselli_, Nov 17 2013]
%t Numerator[Convergents[Sqrt[591], 30]] (* _Vincenzo Librandi_, Nov 17 2013 *)
%t CoefficientList[Series[(24 + 73 x + 316 x^2 + 389 x^3 + 705 x^4 + 5324 x^5 + 6029 x^6 + 11353 x^7 + 51441 x^8 + 165676 x^9 + 51441 x^10 - 11353 x^11 + 6029 x^12 - 5324 x^13 + 705 x^14 - 389 x^15 + 316 x^16 - 73 x^17 + 24 x^18 - x^19)/(1 - 331352 x^10 + x^20), {x, 0, 30}], x] (* _Bruno Berselli_, Nov 17 2013 *)
%Y Cf. A042133.
%K nonn,cofr,frac,easy,less
%O 0,1
%A _N. J. A. Sloane_.
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