OFFSET
1,2
COMMENTS
Starting with a unit square, circumscribe a pentagon outside the square, another square around the pentagon and so on. This is same as polygon circumscribing but using only squares and pentagons with eccentric allowable.
Odd terms are square areas, even terms are pentagon ones.
LINKS
Kival Ngaokrajang, Squares and pentagons arrange in successively circumscribing for n = 1..10
Eric Weisstein's World of Mathematics, Polygon Circumscribing
FORMULA
a(n) = round(x(n)), x(1) = 1, x(2) = (5/(4*t3)) * (((1/2) + t1/((t1/t2)+1))/s1)^2, for n >= 3, x(n) = x(n-2) * k, where k = (1 + 2*t1*t2/(t1+t2))^2, t1 = tan(Pi/10), t2 = tan(3*Pi/10), t3 = tan(Pi/5), s1 = sin(3*Pi/10).
PROG
(Small Basic)
t1=math.Tan(Math.Pi/10)
t2=math.Tan(3*Math.Pi/10)
t3=Math.Tan(Math.Pi/5)
s1=math.Sin(3*Math.Pi/10)
k=math.Power((1+2*t1*t2/(t1+t2)), 2)
x[1]=1
x[2]=(5/(4*t3))*Math.Power(((1/2+t1/((t1/t2)+1))/s1), 2)
For n = 3 To 50
x[n]=x[n-2]*k
EndFor
For i = 1 To 50
TextWindow.Write(i+" ")
TextWindow.Write(math.Round(x[i])+" ")
TextWindow.WriteLine(" ")
EndFor
CROSSREFS
KEYWORD
nonn
AUTHOR
Kival Ngaokrajang, Mar 12 2013
EXTENSIONS
a(26) corrected by Bill McEachen, Oct 28 2023
STATUS
approved