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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

%I

%S 14,26,38,58,70,82,98,110,122,142,154,166,182,194,206,218,238,250,262,

%T 278,290,302,322,334,346,362,374,386,398,418,430,442,458,470,482,502,

%U 514,526,542,554,566,578,598,610,622,638,650,662,682,694,706,722,734,746,766,778,790

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

%C 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 Kival Ngaokrajang, <a href="/A242395/a242395.pdf">Illustration of initial terms</a>

%o (Small Basic)

%o a[0]=3

%o iy=0

%o For n = 1 To 100

%o r=n/(math.Power(3,0.5)/2)

%o If r-math.Floor(r)>=0.5 Then

%o ix=1

%o Else

%o ix=0

%o EndIf

%o If n=1 Then

%o d1=0

%o Else

%o If ix=iy Then

%o d1=3

%o Else

%o if ix=1 and iy=0 Then

%o d1=5

%o Else

%o d1=4

%o EndIf

%o EndIf

%o EndIf

%o iy=ix

%o a[n]=a[n-1]+d1

%o TextWindow.Write(2*(2*a[n]+1)+", ")

%o EndFor

%Y Cf. A242118.

%K nonn

%O 1,1

%A _Kival Ngaokrajang_, May 13 2014

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Last modified June 15 15:16 EDT 2021. Contains 345049 sequences. (Running on oeis4.)