A042730 - OEIS

%I #17 Sep 08 2022 08:44:55

%S 29,30,329,359,21151,21510,236251,257761,15186389,15444150,169627889,

%T 185072039,10903806151,11088878190,121792588051,132881466241,

%U 7828917630029,7961799096270,87446908592729,95408707688999,5621151954554671,5716560662243670,62786758576991371

%N Numerators of continued fraction convergents to sqrt(895).

%H Vincenzo Librandi, <a href="/A042730/b042730.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, 718, 0, 0, 0, -1).

%F G.f.: (29 +30*x +329*x^2 +359*x^3 +329*x^4 -30*x^5 +29*x^6 -x^7)/(1 -718*x^4 +x^8). - _Vincenzo Librandi_, Dec 03 2013

%F a(n) = 718*a(n-4) - a(n-8). - _Vincenzo Librandi_, Dec 03 2013

%t Numerator[Convergents[Sqrt[895], 30]] (* or *) CoefficientList[Series[(29 + 30 x + 329 x^2 + 359 x^3 + 329 x^4 - 30 x^5 + 29 x^6 - x^7)/(1 - 718 x^4 + x^8), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 03 2013 *)

%o (Magma) I:=[29, 30, 329, 359, 21151, 21510, 236251, 257761]; [n le 8 select I[n] else 718*Self(n-4)-Self(n-8): n in [1..30]]; // _Vincenzo Librandi_, Dec 03 2013

%Y Cf. A042731.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.

%E More terms from _Vincenzo Librandi_, Dec 03 2013