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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 (list; graph; refs; listen; history; text; internal format)
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 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
KEYWORD
nonn
AUTHOR
Kival Ngaokrajang, May 13 2014
STATUS
approved

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Last modified May 30 18:48 EDT 2024. Contains 372974 sequences. (Running on oeis4.)