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%I #15 Sep 08 2022 08:44:55
%S 29,30,89,297,1871,5910,13691,19601,1150549,1170150,3490849,11642697,
%T 73347031,231683790,536714611,768398401,45103821869,45872220270,
%U 136848262409,456417007497,2875350307391,9082467929670
%N Numerators of continued fraction convergents to sqrt(882).
%H Vincenzo Librandi, <a href="/A042704/b042704.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,39202,0,0,0,0,0,0,0,-1).
%F G.f.: (29 +30*x +89*x^2 +297*x^3 +1871*x^4 +5910*x^5 +13691*x^6 +19601*x^7 +13691*x^8 -5910*x^9 +1871*x^10 -297*x^11 +89*x^12 -30*x^13 +29*x^14 -x^15)/(1 -39202*x^8 +x^16). - _Vincenzo Librandi_, Dec 02 2013
%F a(n) = 39202*a(n-8) - a(n-16). - _Vincenzo Librandi_, Dec 02 2013
%t Numerator[Convergents[Sqrt[882], 30]] (* or *) CoefficientList[Series[(29 + 30 x + 89 x^2 + 297 x^3 + 1871 x^4 + 5910 x^5 + 13691 x^6 + 19601 x^7 + 13691 x^8 - 5910 x^9 + 1871 x^10 - 297 x^11 + 89 x^12 - 30 x^13 + 29 x^14 - x^15)/(1 - 39202 x^8 + x^16), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 02 2013 *)
%o (Magma) I:=[29,30,89,297,1871,5910,13691,19601,1150549,1170150,3490849, 11642697,73347031,231683790,536714611,768398401]; [n le 16 select I[n] else 39202*Self(n-8)-Self(n-16): n in [1..30]]; // _Vincenzo Librandi_, Dec 02 2013
%Y Cf. A042705.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
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