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%I #14 Sep 08 2022 08:44:55
%S 30,31,185,216,1481,1697,9966,11663,709746,721409,4316791,5038200,
%T 34545991,39584191,232466946,272051137,16555535166,16827586303,
%U 100693466681,117521052984,805819784585,923340837569,5422523972430,6345864809999,386174412572370,392520277382369
%N Numerators of continued fraction convergents to sqrt(952).
%H Vincenzo Librandi, <a href="/A042842/b042842.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, 23326, 0, 0, 0, 0, 0, 0, 0, -1).
%F G.f.: (30 +31*x +185*x^2 +216*x^3 +1481*x^4 +1697*x^5 +9966*x^6 +11663*x^7 +9966*x^8 -1697*x^9 +1481*x^10 -216*x^11 +185*x^12 -31*x^13 +30*x^14 -x^15)/(1 -23326*x^8 +x^16). - _Vincenzo Librandi_, Dec 07 2013
%F a(n) = 23326*a(n-8) - a(n-16). - _Vincenzo Librandi_, Dec 07 2013
%t Numerator[Convergents[Sqrt[952], 30]] (* or *)CoefficientList[Series[(30 + 31 x + 185 x^2 + 216 x^3 + 1481 x^4 + 1697 x^5 + 9966 x^6 + 11663 x^7 + 9966 x^8 - 1697 x^9 + 1481 x^10 - 216 x^11 + 185 x^12 - 31 x^13 + 30 x^14 - x^15)/(1 - 23326 x^8 + x^16), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 07 2013 *)
%o (Magma) I:=[30, 31, 185, 216, 1481, 1697, 9966, 11663, 709746, 721409, 4316791, 5038200, 34545991, 39584191, 232466946, 272051137]; [n le 16 select I[n] else 23326*Self(n-8)-Self(n-16): n in [1..30]]; // _Vincenzo Librandi_, Dec 07 2013
%Y Cf. A042843.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
%E More terms from _Vincenzo Librandi_, Dec 07 2013
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