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A042708 Numerators of continued fraction convergents to sqrt(884). 2

%I #21 Sep 08 2022 08:44:55

%S 29,30,89,119,327,446,1219,1665,97789,99454,296697,396151,1088999,

%T 1485150,4059299,5544449,325637341,331181790,988000921,1319182711,

%U 3626366343,4945549054,13517464451,18463013505,1084372247741,1102835261246,3290042770233,4392878031479

%N Numerators of continued fraction convergents to sqrt(884).

%H Vincenzo Librandi, <a href="/A042708/b042708.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 (0,0,0,0,0,0,0,3330,0,0,0,0,0,0,0,-1).

%F G.f.: -(x^15 -29*x^14 +30*x^13 -89*x^12 +119*x^11 -327*x^10 +446*x^9 -1219*x^8 -1665*x^7 -1219*x^6 -446*x^5 -327*x^4 -119*x^3 -89*x^2 -30*x -29) / (x^16 -3330*x^8 +1). - _Colin Barker_, Nov 09 2013

%F a(n) = 3330*a(n-8) - a(n-16). - _Vincenzo Librandi_, Dec 02 2013

%t Numerator[Convergents[Sqrt[884],30]] (* _Harvey P. Dale_, Nov 16 2011 *)

%t CoefficientList[Series[-(x^15 - 29 x^14 + 30 x^13 - 89 x^12 + 119 x^11 - 327 x^10 + 446 x^9 - 1219 x^8 - 1665 x^7 - 1219 x^6 - 446 x^5 - 327 x^4 - 119 x^3 - 89 x^2 - 30 x - 29)/(x^16 - 3330 x^8 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 02 2013 *)

%o (Magma) I:=[29,30,89,119,327,446,1219,1665,97789,99454,296697,396151, 1088999,1485150,4059299,5544449]; [n le 16 select I[n] else 3330*Self(n-8)-Self(n-16): n in [1..30]]; // _Vincenzo Librandi_, Dec 02 2013

%Y Cf. A042709.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 09 2013

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Last modified July 14 05:06 EDT 2024. Contains 374291 sequences. (Running on oeis4.)