A242396 - OEIS

%I #18 May 31 2014 14:49:39

%S 4,6,8,10,12,14,18,20,22,24,26,28,32,34,36,38,40,42,44,48,50,52,54,56,

%T 58,62,64,66,68,70,72,74,78,80,82,84,86,88,92,94,96,98,100,102,104,

%U 108,110,112,114,116,118,122,124,126,128,130,132,134,138,140,142

%N Number of rows of equilateral triangles (sides length = 1) that intersect the circumference of a circle of radius n centered at (0,0) or (1/2,0).

%C See crossreferenced sequences for illustrations.

%F G.f., conjectured: (-2*x^14 + 4*x^13 + 2*x^12 + 2*x^11 + 2*x^10 + 2*x^9 + 2*x^8 + 4*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 4*x)/(x^14 - x^13 - x + 1). - _Ralf Stephan_, May 18 2014

%F Asymptotics from g.f.: a(n) ~ 30/13 * n. - _Ralf Stephan_, May 18 2014

%o (Small Basic)

%o For n =1 To 100

%o   r6=n*math.Sin(30*Math.Pi/180)/(Math.Power(3,0.5)/2)

%o   r6a=math.Round(r6)

%o   If r6-math.Floor(r6) > 0.5 Then

%o     a=r6a*4

%o   Else

%o     a=2*(r6a*2+1)

%o   EndIf

%o   TextWindow.Write(a+", ")

%o EndFor

%Y Cf. A242394, A242395.

%K nonn

%O 1,1

%A _Kival Ngaokrajang_, May 13 2014