A041325 - OEIS

%I #16 Apr 30 2023 11:24:38

%S 1,3,4,15,394,1197,1591,5970,156811,476403,633214,2376045,62410384,

%T 189607197,252017581,945659940,24839176021,75463188003,100302364024,

%U 376370280075,9885929645974,30034159217997,39920088863971,149794425809910,3934575159921631

%N Denominators of continued fraction convergents to sqrt(176).

%H Vincenzo Librandi, <a href="/A041325/b041325.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 (0,0,0,398,0,0,0,-1).

%F G.f.: -(x^2-3*x-1)*(x^4+5*x^2+1) / ((x^4-20*x^2+1)*(x^4+20*x^2+1)). - _Colin Barker_, Nov 15 2013

%F a(n) = 398*a(n-4) - a(n-8). - _Vincenzo Librandi_, Dec 15 2013

%t Denominator[Convergents[Sqrt[176], 30]] (* _Vincenzo Librandi_, Dec 15 2013 *)

%t LinearRecurrence[{0,0,0,398,0,0,0,-1},{1,3,4,15,394,1197,1591,5970},30] (* _Harvey P. Dale_, Apr 30 2023 *)

%o (Magma) I:=[1,3,4,15,394,1197,1591,5970]; [n le 8 select I[n] else 398*Self(n-4)-Self(n-8): n in [1..40]]; // _Vincenzo Librandi_, Dec 15 2013

%Y Cf. A041324, A010220.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 15 2013