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%I #16 Sep 08 2022 08:44:55
%S 27,55,137,192,521,713,1947,4607,250725,506057,1262839,1768896,
%T 4800631,6569527,17939685,42448897,2310180123,4662809143,11635798409,
%U 16298607552,44233013513,60531621065,165296255643
%N Numerators of continued fraction convergents to sqrt(752).
%H Vincenzo Librandi, <a href="/A042448/b042448.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 (0,0,0,0,0,0,0,9214,0,0,0,0,0,0,0,-1).
%F G.f.: (27 +55*x +137*x^2 +192*x^3 +521*x^4 +713*x^5 +1947*x^6 +4607*x^7 +1947*x^8 -713*x^9 +521*x^10 -192*x^11 +137*x^12 -55*x^13 +27*x^14 -x^15)/(1 -9214*x^8 +x^16). - _Vincenzo Librandi_, Nov 25 2013
%F a(n) = 9214*a(n-8) - a(n-16). - _Vincenzo Librandi_, Nov 25 2013
%t Numerator[Convergents[Sqrt[752], 30]] (* or *) CoefficientList[Series[(27 + 55 x + 137 x^2 + 192 x^3 + 521 x^4 + 713 x^5 + 1947 x^6 + 4607 x^7 + 1947 x^8 - 713 x^9 + 521 x^10 - 192 x^11 + 137 x^12 - 55 x^13 + 27 x^14 - x^15)/(1 - 9214 x^8 + x^16), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 24 2013 *)
%o (Magma) I:=[27,55,137,192,521,713,1947,4607,250725,506057,1262839, 1768896, 4800631,6569527,17939685,42448897]; [n le 16 select I[n] else 9214*Self(n-8)-Self(n-16): n in [1..30]]; // _Vincenzo Librandi_, Nov 25 2013
%Y Cf. A042449.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.