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Numerators of continued fraction convergents to sqrt(642).
2

%I #15 Sep 08 2022 08:44:55

%S 25,51,76,1875,1951,5777,290801,587379,878180,21663699,22541879,

%T 66747457,3359914729,6786576915,10146491644,250302376371,260448868015,

%U 771200112401,38820454488065,78412109088531

%N Numerators of continued fraction convergents to sqrt(642).

%H Vincenzo Librandi, <a href="/A042232/b042232.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 (0,0,0,0,0,11554,0,0,0,0,0,-1).

%F G.f.: (25 +51*x +76*x^2 +1875*x^3 +1951*x^4 +5777*x^5 +1951*x^6 -1875*x^7 +76*x^8 -51*x^9 +25*x^10 -x^11)/(1 -11554*x^6 +x^12). - _Vincenzo Librandi_, Nov 19 2013

%F a(n) = 11554*a(n-6) - a(n-12). - _Vincenzo Librandi_, Nov 19 2013

%t Numerator[Convergents[Sqrt[642], 30]] (* or *) CoefficientList[Series[(25 + 51 x + 76 x^2 + 1875 x^3 + 1951 x^4 + 5777 x^5 + 1951 x^6 - 1875 x^7 + 76 x^8 - 51 x^9 + 25 x^10 - x^11)/(1 - 11554 x^6 + x^12), {x, 0, 20}], x] (* _Vincenzo Librandi_, Nov 19 2013 *)

%o (Magma) I:=[25,51,76,1875,1951,5777,290801,587379,878180,21663699,22541879, 66747457]; [n le 12 select I[n] else 11554*Self(n-6)-Self(n-12): n in [1..30]]; // _Vincenzo Librandi_, Nov 19 2013

%Y Cf. A042233.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.