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%I #18 Sep 08 2022 08:44:55
%S 29,30,59,89,5221,5310,10531,15841,929309,945150,1874459,2819609,
%T 165411781,168231390,333643171,501874561,29442367709,29944242270,
%U 59386609979,89330852249,5240576040421,5329906892670
%N Numerators of continued fraction convergents to sqrt(880).
%H Vincenzo Librandi, <a href="/A042700/b042700.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 (0,0,0,178,0,0,0,-1).
%F G.f.: (29 +30*x +59*x^2 +89*x^3 +59*x^4 -30*x^5 +29*x^6 -x^7)/(1 -178*x^4 +x^8). - _Vincenzo Librandi_, Dec 02 2013
%F a(n) = 178*a(n-4) - a(n-8). - _Vincenzo Librandi_, Dec 02 2013
%t Numerator[Convergents[Sqrt[880], 30]]
%t (* or *)
%t CoefficientList[Series[(29 + 30 x + 59 x^2 + 89 x^3 + 59 x^4 - 30 x^5 + 29 x^6 - x^7)/(1 - 178 x^4 + x^8), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 02 2013 *)
%t LinearRecurrence[{0,0,0,178,0,0,0,-1},{29,30,59,89,5221,5310,10531,15841},30] (* _Harvey P. Dale_, Mar 27 2022 *)
%o (Magma) I:=[29, 30, 59, 89, 5221, 5310, 10531, 15841]; [n le 8 select I[n] else 178*Self(n-4)-Self(n-8): n in [1..30]]; // _Vincenzo Librandi_, Dec 02 2013
%Y Cf. A042701.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
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