

A242395


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


4



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
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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



PROG

(Small Basic)
a[0]=3
iy=0
For n = 1 To 100
r=n/(math.Power(3, 0.5)/2)
If rmath.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[n1]+d1
TextWindow.Write(2*(2*a[n]+1)+", ")
EndFor


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



