cp's OEIS Frontend

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

%I A242395 #9 May 18 2014 11:14:08
%S A242395 14,26,38,58,70,82,98,110,122,142,154,166,182,194,206,218,238,250,262,
%T A242395 278,290,302,322,334,346,362,374,386,398,418,430,442,458,470,482,502,
%U A242395 514,526,542,554,566,578,598,610,622,638,650,662,682,694,706,722,734,746,766,778,790
%N A242395 Number of equilateral triangles (sides length = 1) that intersect the circumference of a circle of radius n centered at (1/2,0).
%C A242395 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.
%H A242395 Kival Ngaokrajang, <a href="/A242395/a242395.pdf">Illustration of initial terms</a>
%o A242395 (Small Basic)
%o A242395 a[0]=3
%o A242395 iy=0
%o A242395 For n = 1 To 100
%o A242395    r=n/(math.Power(3,0.5)/2)
%o A242395    If r-math.Floor(r)>=0.5 Then
%o A242395      ix=1
%o A242395    Else
%o A242395      ix=0
%o A242395    EndIf
%o A242395    If n=1 Then
%o A242395      d1=0
%o A242395    Else
%o A242395      If ix=iy Then
%o A242395        d1=3
%o A242395      Else
%o A242395        if ix=1 and iy=0 Then
%o A242395          d1=5
%o A242395        Else
%o A242395          d1=4
%o A242395        EndIf
%o A242395      EndIf
%o A242395    EndIf
%o A242395    iy=ix
%o A242395    a[n]=a[n-1]+d1
%o A242395    TextWindow.Write(2*(2*a[n]+1)+", ")
%o A242395 EndFor
%Y A242395 Cf. A242118.
%K A242395 nonn
%O A242395 1,1
%A A242395 _Kival Ngaokrajang_, May 13 2014