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%I #18 Sep 08 2022 08:44:55
%S 30,31,61,153,979,2111,3090,5201,315150,320351,635501,1591353,
%T 10183619,21958591,32142210,54100801,3278190270,3332291071,6610481341,
%U 16553253753,105930003859,228413261471,334343265330,562756526801,34099734873390,34662491400191,68762226273581
%N Numerators of continued fraction convergents to sqrt(936).
%H Vincenzo Librandi, <a href="/A042810/b042810.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 10402, 0, 0, 0, 0, 0, 0, 0, -1).
%F G.f.: (30 +31*x +61*x^2 +153*x^3 +979*x^4 +2111*x^5 +3090*x^6 +5201*x^7 +3090*x^8 -2111*x^9 +979*x^10 -153*x^11 +61*x^12 -31*x^13 +30*x^14 -x^15)/(1 -10402*x^8 +x^16). - _Vincenzo Librandi_, Dec 05 2013
%F a(n) = 10402*a(n-8) - a(n-16). - _Vincenzo Librandi_, Dec 05 2013
%t Numerator[Convergents[Sqrt[936], 30]] (* _Harvey P. Dale_, Feb 06 2012 *)
%t CoefficientList[Series[(30 + 31 x + 61 x^2 + 153 x^3 + 979 x^4 + 2111 x^5 + 3090 x^6 + 5201 x^7 + 3090 x^8 - 2111 x^9 + 979 x^10 - 153 x^11 + 61 x^12 - 31 x^13 + 30 x^14 - x^15)/(1 - 10402 x^8 + x^16), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 05 2013 *)
%o (Magma) I:=[30, 31, 61, 153, 979, 2111, 3090, 5201, 315150, 320351, 635501, 1591353, 10183619, 21958591, 32142210, 54100801]; [n le 16 select I[n] else 10402*Self(n-8)-Self(n-16): n in [1..30]]; // _Vincenzo Librandi_, Dec 05 2013
%Y Cf. A042811.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
%E More terms from _Vincenzo Librandi_, Dec 05 2013