A242396 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).

4, 6, 8, 10, 12, 14, 18, 20, 22, 24, 26, 28, 32, 34, 36, 38, 40, 42, 44, 48, 50, 52, 54, 56, 58, 62, 64, 66, 68, 70, 72, 74, 78, 80, 82, 84, 86, 88, 92, 94, 96, 98, 100, 102, 104, 108, 110, 112, 114, 116, 118, 122, 124, 126, 128, 130, 132, 134, 138, 140, 142

Offset

1,1

Comments

See crossreferenced sequences for illustrations.

Links

Table of n, a(n) for n=1..61.

Formula

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

Asymptotics from g.f.: a(n) ~ 30/13 * n. - Ralf Stephan, May 18 2014

Prog

(Small Basic)
For n =1 To 100
  r6=n*math.Sin(30*Math.Pi/180)/(Math.Power(3, 0.5)/2)
  r6a=math.Round(r6)
  If r6-math.Floor(r6) > 0.5 Then
    a=r6a*4
  Else
    a=2*(r6a*2+1)
  EndIf
  TextWindow.Write(a+", ")
EndFor

Crossrefs

Cf. A242394, A242395.

Sequence in context: A289426 A186331 A258036 * A061344 A066664 A064938

Adjacent sequences: A242393 A242394 A242395 * A242397 A242398 A242399

Keyword

nonn

Author

Kival Ngaokrajang, May 13 2014

Status

approved