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A042508 Numerators of continued fraction convergents to sqrt(782). 2

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

%S 27,28,755,783,43037,43820,1182357,1226177,67395915,68622092,

%T 1851570307,1920192399,105541959853,107462152252,2899557918405,

%U 3007020070657,165278641733883,168285661804540,4540705848651923

%N Numerators of continued fraction convergents to sqrt(782).

%H Vincenzo Librandi, <a href="/A042508/b042508.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 (0,0,0,1566,0,0,0,-1).

%F G.f.: (27 +28*x +755*x^2 +783*x^3 +755*x^4 -28*x^5 +27*x^6 -x^7)/(1 -1566*x^4 +x^8). - _Vincenzo Librandi_, Nov 26 2013

%F a(n) = 1566*a(n-4) - a(n-8). - _Vincenzo Librandi_, Nov 26 2013

%t Numerator[Convergents[Sqrt[782], 30]] (* or *) CoefficientList[Series[(27 + 28 x + 755 x^2 + 783 x^3 + 755 x^4 - 28 x^5 + 27 x^6 - x^7)/(1 - 1566 x^4 + x^8), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 25 2013 *)

%o (Magma) I:=[27, 28, 755, 783, 43037, 43820, 1182357, 1226177]; [n le 8 select I[n] else 1566*Self(n-4)-Self(n-8): n in [1..30]]; // _Vincenzo Librandi_, Nov 26 2013

%Y Cf. A042509.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.

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Last modified March 29 08:53 EDT 2024. Contains 371268 sequences. (Running on oeis4.)