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A041595 Denominators of continued fraction convergents to sqrt(315). 2

%I

%S 1,1,3,4,139,143,425,568,19737,20305,60347,80652,2802515,2883167,

%T 8568849,11452016,397937393,409389409,1216716211,1626105620,

%U 56504307291,58130412911,172765133113,230895546024,8023213697929,8254109243953,24531432185835,32785541429788

%N Denominators of continued fraction convergents to sqrt(315).

%H Vincenzo Librandi, <a href="/A041595/b041595.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 (0,0,0,142,0,0,0,-1).

%F G.f.: -(x^2-x-1)*(x^4+4*x^2+1) / ((x^4-12*x^2+1)*(x^4+12*x^2+1)). - _Colin Barker_, Nov 19 2013

%F a(n) = 142*a(n-4) - a(n-8) for n>7, - _Vincenzo Librandi_, Dec 21 2013

%t Denominator[Convergents[Sqrt[315], 30]] (* _Vincenzo Librandi_, Dec 21 2013 *)

%o (MAGMA) I:=[1,1,3,4,139,143,425,568]; [n le 8 select I[n] else 142*Self(n-4)-Self(n-8): n in [1..40]]; // _Vincenzo Librandi_, Dec 21 2013

%Y Cf. A041594, A040297.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 19 2013

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Last modified March 26 01:08 EDT 2019. Contains 321479 sequences. (Running on oeis4.)