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Denominators of continued fraction convergents to sqrt(232).
2

%I #16 Sep 08 2022 08:44:54

%S 1,4,13,95,298,1287,38908,156919,509665,3724574,11683387,50458122,

%T 1525427047,6152166310,19981925977,146025648149,458058870424,

%U 1978261129845,59805892765774,241201832192941,783411389344597,5725081557605120,17958656062159957

%N Denominators of continued fraction convergents to sqrt(232).

%H Vincenzo Librandi, <a href="/A041433/b041433.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 (0,0,0,0,0,39206,0,0,0,0,0,-1).

%F G.f.: -(x^10-4*x^9+13*x^8-95*x^7+298*x^6-1287*x^5-298*x^4-95*x^3-13*x^2-4*x-1) / ((x^6-198*x^3-1)*(x^6+198*x^3-1)). - _Colin Barker_, Nov 17 2013

%F a(n) = 39206*a(n-6) - a(n-12) for n>7. - _Vincenzo Librandi_, Dec 17 2013

%t Denominator[Convergents[Sqrt[232], 30]] (* _Vincenzo Librandi_, Dec 17 2013 *)

%o (Magma) I:=[1,4,13,95,298,1287,38908,156919,509665, 3724574,11683387,50458122]; [n le 12 select I[n] else 39206*Self(n-6)-Self(n-12): n in [1..40]]; // _Vincenzo Librandi_, Dec 17 2013

%Y Cf. A041432, A040216.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 17 2013