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%I #17 Sep 08 2022 08:44:55
%S 24,49,73,122,561,683,3293,3976,7269,18514,895941,1810396,2706337,
%T 4516733,20773269,25290002,121933277,147223279,269156556,685536391,
%U 33174903324,67035343039,100210246363
%N Numerators of continued fraction convergents to sqrt(595).
%H Vincenzo Librandi, <a href="/A042140/b042140.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 (0,0,0,0,0,0,0,0,0,37028,0,0,0,0,0,0,0,0,0,-1).
%F From _Vincenzo Librandi_, Nov 18 2013: (Start)
%F G.f.: (24 +49*x +73*x^2 +122*x^3 +561*x^4 +683*x^5 +3293*x^6 +3976*x^7 +7269*x^8 +18514*x^9 +7269*x^10 -3976*x^11 +3293*x^12 -683*x^13 +561*x^14 -122*x^15 +73*x^16 -49*x^17 +24*x^18 -x^19)/(1 -37028*x^10 +x^20).
%F a(n) = 37028*a(n-10) - a(n-20). (End)
%t Numerator[Convergents[Sqrt[595], 30]] (* or *) CoefficientList[Series[(24 + 49 x + 73 x^2 + 122 x^3 + 561 x^4 + 683 x^5 + 3293 x^6 + 3976 x^7 + 7269 x^8 + 18514 x^9 + 7269 x^10 - 3976 x^11 + 3293 x^12 - 683 x^13 + 561 x^14 - 122 x^15 + 73 x^16 - 49 x^17 + 24 x^18 - x^19)/(1 - 37028 x^10 + x^20), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 18 2013 *)
%o (Magma) I:=[24,49,73,122,561,683,3293,3976,7269,18514,895941,1810396, 2706337,4516733,20773269,25290002,121933277,147223279,269156556, 685536391]; [n le 20 select I[n] else 37028*Self(n-10)-Self(n-20): n in [1..30]]; // _Vincenzo Librandi_, Nov 18 2013
%Y Cf. A042141.
%K nonn,cofr,frac,easy,less
%O 0,1
%A _N. J. A. Sloane_.