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%I #18 Sep 08 2022 08:44:55
%S 25,176,1081,7743,388231,2725360,16740391,119908097,6012145241,
%T 42204924784,259241693945,1856896782399,93104080813895,
%U 653585462479664,4014616855691879,28755903452322817,1441809789471832729
%N Numerators of continued fraction convergents to sqrt(632).
%H Vincenzo Librandi, <a href="/A042212/b042212.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 (0,0,0,15486,0,0,0,-1).
%F G.f.: (25 + 176*x + 1081*x^2 + 7743*x^3 + 1081*x^4 - 176*x^5 + 25*x^6 - x^7)/(1 - 15486*x^4 + x^8). - _Vincenzo Librandi_, Nov 19 2013
%F a(n) = 15486*a(n-4) - a(n-8). - _Vincenzo Librandi_, Nov 19 2013
%t Numerator[Convergents[Sqrt[632], 20]] (* _Harvey P. Dale_, Aug 06 2013 *)
%t CoefficientList[Series[(25 + 176 x + 1081 x^2 + 7743 x^3 + 1081 x^4 - 176 x^5 + 25 x^6 - x^7)/(1 - 15486 x^4 + x^8), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 19 2013 *)
%o (Magma) I:=[25,176,1081,7743,388231,2725360,16740391,119908097]; [n le 8 select I[n] else 15486*Self(n-4)-Self(n-8): n in [1..30]]; // _Vincenzo Librandi_, Nov 19 2013
%Y Cf. A042213.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
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