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A041449 Denominators of continued fraction convergents to sqrt(240).

%I A041449 #29 Sep 08 2022 08:44:54
%S A041449 1,2,61,124,3781,7686,234361,476408,14526601,29529610,900414901,
%T A041449 1830359412,55811197261,113452753934,3459393815281,7032240384496,
%U A041449 214426605350161,435885451084818,13290990137894701,27017865726874220,823826961944121301,1674671789615116822
%N A041449 Denominators of continued fraction convergents to sqrt(240).
%H A041449 Vincenzo Librandi, <a href="/A041449/b041449.txt">Table of n, a(n) for n = 0..200</a>
%H A041449 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,62,0,-1).
%F A041449 G.f.: -(x^2-2*x-1) / ((x^2-8*x+1)*(x^2+8*x+1)). - _Colin Barker_, Nov 17 2013
%F A041449 a(n) = 62*a(n-2) - a(n-4) for n>3. - _Vincenzo Librandi_, Dec 18 2013
%F A041449 From _Gerry Martens_, Jul 11 2015: (Start)
%F A041449 Interspersion of 2 sequences [a0(n-1),a1(n-1)] for n>0:
%F A041449 a0(n) = sqrt(2+(31-8*sqrt(15))^(2*n+1)+(31+8*sqrt(15))^(2*n+1))/8.
%F A041449 a1(n) = 2*sum(i=0,n,a0(i)). (End)
%t A041449 Denominator[Convergents[Sqrt[240], 30]] (* _Vincenzo Librandi_, Dec 18 2013 *)
%t A041449 a0[n_] := Sqrt[2+(31-8*Sqrt[15])^(1+2*n)+(31+8*Sqrt[15])^(1+2*n)]/8 // Simplify
%t A041449 a1[n_] := 2*Sum[a0[i], {i, 0, n}]
%t A041449 Flatten[MapIndexed[{a0[#-1],a1[#-1]}&,Range[11]]] (* _Gerry Martens_, Jul 10 2015 *)
%o A041449 (Magma) I:=[1,2,61,124]; [n le 4 select I[n] else 62*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Dec 18 2013
%Y A041449 Cf. A041448, A040224.
%K A041449 nonn,frac,easy
%O A041449 0,2
%A A041449 _N. J. A. Sloane_
%E A041449 More terms from _Colin Barker_, Nov 17 2013