A042528 - OEIS

%I #13 Sep 08 2022 08:44:55

%S 28,169,704,4393,246712,1484665,6185372,38596897,2167611604,

%T 13044266521,54344677688,339112332649,19044635306032,114606924168841,

%U 477472331981396,2979440916057217,167326163631185548,1006936422703170505

%N Numerators of continued fraction convergents to sqrt(793).

%H Vincenzo Librandi, <a href="/A042528/b042528.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 (0,0,0,8786,0,0,0,-1).

%F G.f.: (28 +169*x +704*x^2 +4393*x^3 +704*x^4 -169*x^5 +28*x^6 -x^7)/(1 -8786*x^4 +x^8). - _Vincenzo Librandi_, Nov 26 2013

%F a(n) = 8786*a(n-4) - a(n-8). - _Vincenzo Librandi_, Nov 26 2013

%t Numerator[Convergents[Sqrt[793], 30]] (* or *) CoefficientList[Series[(28 + 169 x + 704 x^2 + 4393 x^3 + 704 x^4 - 169 x^5 + 28 x^6 - x^7)/(1 - 8786 x^4 + x^8), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 25 2013 *)

%o (Magma) I:=[28, 169, 704, 4393, 246712, 1484665, 6185372, 38596897]; [n le 8 select I[n] else 8786*Self(n-4)-Self(n-8): n in [1..30]]; // _Vincenzo Librandi_, Nov 26 2013

%Y Cf. A042529.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.