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%I #18 Jun 26 2022 23:42:25
%S 31,249,280,1929,2209,19601,1217471,9759369,10976840,75620409,
%T 86597249,768398401,47727298111,382586783289,430314081400,
%U 2964471271689,3394785353089,30122754096401,1871005539329951,14998167068736009,16869172608065960,116213202717131769
%N Numerators of continued fraction convergents to sqrt(968).
%H Vincenzo Librandi, <a href="/A042872/b042872.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 39202, 0, 0, 0, 0, 0, -1).
%F G.f.: (31 + 249*x + 280*x^2 + 1929*x^3 + 2209*x^4 + 19601*x^5 + 2209*x^6 - 1929*x^7 + 280*x^8 - 249*x^9 + 31*x^10 - x^11)/(1 - 39202*x^6 + x^12). - _Vincenzo Librandi_, Dec 08 2013
%F a(n) = 39202*a(n-6) - a(n-12). - _Vincenzo Librandi_, Dec 08 2013
%t Numerator[Convergents[Sqrt[968], 30]] (* or *) CoefficientList[Series[(31 + 249 x + 280 x^2 + 1929 x^3 + 2209 x^4 + 19601 x^5 + 2209 x^6 - 1929 x^7 + 280 x^8 -249 x^9 + 31 x^10 - x^11)/(1 - 39202 x^6 + x^12), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 08 2013 *)
%t LinearRecurrence[{0,0,0,0,0,39202,0,0,0,0,0,-1},{31,249,280,1929,2209,19601,1217471,9759369,10976840,75620409,86597249,768398401},30] (* _Harvey P. Dale_, Oct 17 2018 *)
%o (Magma) I:=[ 31, 249, 280, 1929, 2209, 19601, 1217471, 9759369, 10976840, 75620409, 86597249, 768398401]; [n le 12 select I[n] else 39202*Self(n-6)-Self(n-12): n in [1..30]]; // _Vincenzo Librandi_, Dec 08 2013
%Y Cf. A042873.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_
%E More terms from _Vincenzo Librandi_, Dec 08 2013
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