A242395 Number of equilateral triangles (sides length = 1) that intersect the circumference of a circle of radius n centered at (1/2,0).

14, 26, 38, 58, 70, 82, 98, 110, 122, 142, 154, 166, 182, 194, 206, 218, 238, 250, 262, 278, 290, 302, 322, 334, 346, 362, 374, 386, 398, 418, 430, 442, 458, 470, 482, 502, 514, 526, 542, 554, 566, 578, 598, 610, 622, 638, 650, 662, 682, 694, 706, 722, 734, 746, 766, 778, 790

Offset

1,1

Comments

For all n, it seems to be the case that transits of the circumference occurring exactly at the corners do not exist. The pattern repeats itself at a half circle. The triangle count in a quadrant by rows can be arranged as an irregular triangle as shown in the illustration. The rows count (A242396) is equal to the case centered at (0,0), A242394.

Links

Table of n, a(n) for n=1..57.

Kival Ngaokrajang, Illustration of initial terms

Prog

(Small Basic)
a[0]=3
iy=0
For n = 1 To 100
   r=n/(math.Power(3, 0.5)/2)
   If r-math.Floor(r)>=0.5 Then
     ix=1
   Else
     ix=0
   EndIf
   If n=1 Then
     d1=0
   Else
     If ix=iy Then
       d1=3
     Else
       if ix=1 and iy=0 Then
         d1=5
       Else
         d1=4
       EndIf
     EndIf
   EndIf
   iy=ix
   a[n]=a[n-1]+d1
   TextWindow.Write(2*(2*a[n]+1)+", ")
EndFor

Crossrefs

Cf. A242118.

Sequence in context: A240227 A191992 A082773 * A112772 A155505 A086258

Adjacent sequences: A242392 A242393 A242394 * A242396 A242397 A242398

Keyword

nonn

Author

Kival Ngaokrajang, May 13 2014

Status

approved