|
%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
|
