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A042784 Numerators of continued fraction convergents to sqrt(923). 2

%I

%S 30,61,91,152,243,638,38523,77684,116207,193891,310098,814087,

%T 49155318,99124723,148280041,247404764,395684805,1038774374,

%U 62722147245,126483068864,189205216109,315688284973,504893501082,1325475287137,80033410729302

%N Numerators of continued fraction convergents to sqrt(923).

%H Vincenzo Librandi, <a href="/A042784/b042784.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, 1276, 0, 0, 0, 0, 0, -1).

%F G.f.: (30 +61*x +91*x^2 +152*x^3 +243*x^4 +638*x^5 +243*x^6 -152*x^7 +91*x^8 -61*x^9 +30*x^10 -x^11)/(1 -1276*x^6 +x^12). - _Vincenzo Librandi_, Dec 04 2013

%F a(n) = 1276*a(n-6) - a(n-12). - _Vincenzo Librandi_, Dec 04 2013

%t Numerator[Convergents[Sqrt[923], 30]] (* or *) CoefficientList[Series[(30 + 61 x + 91 x^2 + 152 x^3 + 243 x^4 + 638 x^5 + 243 x^6 - 152 x^7 + 91 x^8 - 61 x^9 + 30 x^10 - x^11)/(1 - 1276 x^6 + x^12), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 04 2013 *)

%o (MAGMA) I:=[30, 61, 91, 152, 243, 638, 38523, 77684, 116207, 193891, 310098, 814087]; [n le 12 select I[n] else 1276*Self(n-6)-Self(n-12): n in [1..30]]; // _Vincenzo Librandi_, Dec 04 2013

%Y Cf. A042785.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_

%E More terms from _Vincenzo Librandi_, Dec 04 2013

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Last modified April 19 16:18 EDT 2019. Contains 322282 sequences. (Running on oeis4.)