A042400 - OEIS

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

%S 26,27,701,728,38557,39285,1020682,1059967,56138966,57198933,

%T 1486112291,1543311224,81738295939,83281607163,2163778475014,

%U 2247060082177,119010902748218,121257962830395,3150459973508093

%N Numerators of continued fraction convergents to sqrt(727).

%H Vincenzo Librandi, <a href="/A042400/b042400.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 1456, 0, 0, 0, -1).

%F G.f.: (26 +27*x +701*x^2 +728*x^3 +701*x^4 -27*x^5 +26*x^6 -x^7)/(1 -1456*x^4 +x^8). - _Vincenzo Librandi_, Nov 23 2013

%F a(n) = 1456*a(n-4) - a(n-8). - _Vincenzo Librandi_, Nov 23 2013

%t Numerator[Convergents[Sqrt[727], 30]] (* or *) CoefficientList[Series[(26 + 27 x + 701 x^2 + 728 x^3 + 701 x^4 - 27 x^5 + 26 x^6 - x^7)/(1 - 1456 x^4 + x^8), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 23 2013 *)

%o (Magma) I:=[26, 27, 701, 728, 38557, 39285, 1020682, 1059967]; [n le 8 select I[n] else 1456*Self(n-4)-Self(n-8): n in [1..30]]; //  _Vincenzo Librandi_, Nov 23 2013

%Y Cf. A042401.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.