A040634 - OEIS

%I #32 Jul 08 2025 23:35:44

%S 25,1,2,4,2,1,50,1,2,4,2,1,50,1,2,4,2,1,50,1,2,4,2,1,50,1,2,4,2,1,50,

%T 1,2,4,2,1,50,1,2,4,2,1,50,1,2,4,2,1,50,1,2,4,2,1,50,1,2,4,2,1,50,1,2,

%U 4,2,1,50,1,2,4,2,1,50,1,2,4,2,1,50,1,2,4,2,1,50,1,2

%N Continued fraction for sqrt(660).

%C After the first term, periodic with period 6. - _Robert Israel_, Jul 27 2014

%H Vincenzo Librandi, <a href="/A040634/b040634.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Con#confC">Index entries for continued fractions for constants</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 1).

%F G.f.: (25+x+2*x^2+4*x^3+2*x^4+x^5+25*x^6) / (1-x^6). - _Wesley Ivan Hurt_, Jul 29 2014

%p with(numtheory): Digits := 300: convert(evalf(sqrt(660)),confrac);

%t ContinuedFraction[Sqrt[660],100] (* or *) PadRight[{25},100,{50,1,2,4,2,1}] (* _Harvey P. Dale_, Jul 26 2014 *)

%t CoefficientList[Series[(25 + x + 2*x^2 + 4*x^3 + 2*x^4 + x^5 + 25*x^6)/(1 - x^6), {x, 0, 100}], x] (* _Wesley Ivan Hurt_, Jul 29 2014 *)

%t Join[{25},LinearRecurrence[{0, 0, 0, 0, 0, 1},{1, 2, 4, 2, 1, 50},86]] (* _Ray Chandler_, Aug 26 2015 *)

%K nonn,cofr,easy

%O 0,1

%A _N. J. A. Sloane_