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%I #21 Jun 26 2022 23:52:01
%S 31,32,63,536,599,1135,70969,72104,143073,1216688,1359761,2576449,
%T 161099599,163676048,324775647,2761881224,3086656871,5848538095,
%U 365696018761,371544556856,737240575617,6269469161792,7006709737409,13276178899201,830129801487871
%N Numerators of continued fraction convergents to sqrt(994).
%H Vincenzo Librandi, <a href="/A042924/b042924.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, 2270, 0, 0, 0, 0, 0, -1).
%F G.f.: (31 + 32*x + 63*x^2 + 536*x^3 + 599*x^4 + 1135*x^5 + 599*x^6 - 536*x^7 + 63*x^8 - 32*x^9 + 31*x^10 - x^11)/(1 - 2270*x^6 + x^12). - _Vincenzo Librandi_, Dec 09 2013
%F a(n) = 2270*a(n-6) - a(n-12). - _Vincenzo Librandi_, Dec 09 2013
%t Numerator[Convergents[Sqrt[994], 30]] (* or *) CoefficientList[Series[(31 + 32 x + 63 x^2 + 536 x^3 + 599 x^4 + 1135 x^5 + 599 x^6 - 536 x^7 + 63 x^8 - 32 x^9 + 31 x^10 - x^11)/(1 - 2270 x^6 + x^12), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 09 2013 *)
%t LinearRecurrence[{0,0,0,0,0,2270,0,0,0,0,0,-1},{31,32,63,536,599,1135,70969,72104,143073,1216688,1359761,2576449},30] (* _Harvey P. Dale_, Jun 23 2017 *)
%o (Magma) I:=[31,32,63,536,599,1135,70969,72104,143073,1216688,1359761, 2576449]; [n le 12 select I[n] else 2270*Self(n-6)-Self(n-12): n in [1..30]]; // _Vincenzo Librandi_, Dec 09 2013
%Y Cf. A042925.
%K nonn,frac,easy
%O 0,1
%A _N. J. A. Sloane_
%E More terms from _Vincenzo Librandi_, Dec 09 2013