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%I #18 Sep 08 2022 08:44:55
%S 30,31,92,399,8072,32687,73446,106133,6441426,6547559,19536544,
%T 84693735,1713411244,6938338711,15590088666,22528427377,1367295731286,
%U 1389824158663,4146944048612,17977600353111,363698951110832,1472773404796439,3309245760703710,4782019165500149
%N Numerators of continued fraction convergents to sqrt(942).
%H Vincenzo Librandi, <a href="/A042822/b042822.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, 212266, 0, 0, 0, 0, 0, 0, 0, -1).
%F G.f.: (30 +31*x +92*x^2 +399*x^3 +8072*x^4 +32687*x^5 +73446*x^6 +106133*x^7 +73446*x^8 -32687*x^9 +8072*x^10 -399*x^11 +92*x^12 -31*x^13 +30*x^14 -x^15)/(1 -212266*x^8 +x^16). - _Vincenzo Librandi_, Dec 05 2013
%F a(n) = 212266*a(n-8) - a(n-16). - _Vincenzo Librandi_, Dec 05 2013
%t Numerator/@Convergents[Sqrt[942], 30] (* _Harvey P. Dale_, Jul 18 2011 *)
%t CoefficientList[Series[(30 + 31 x + 92 x^2 + 399 x^3 + 8072 x^4 + 32687 x^5 + 73446 x^6 + 106133 x^7 + 73446 x^8 - 32687 x^9 + 8072 x^10 - 399 x^11 + 92 x^12 - 31 x^13 + 30 x^14 - x^15)/(1 - 212266 x^8 + x^16), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 05 2013 *)
%o (Magma) I:=[30, 31, 92, 399, 8072, 32687, 73446, 106133, 6441426, 6547559, 19536544, 84693735, 1713411244, 6938338711, 15590088666, 22528427377]; [n le 16 select I[n] else 212266*Self(n-8)-Self(n-16): n in [1..30]]; // _Vincenzo Librandi_, Dec 05 2013
%Y Cf. A042823.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
%E More terms from _Vincenzo Librandi_, Dec 05 2013
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