login
A216198
Rounded area of squares and pentagons which arrange as successively circumscribing.
1
1, 2, 2, 4, 5, 8, 13, 19, 29, 45, 68, 105, 159, 243, 370, 567, 862, 1319, 2007, 3071, 4673, 7148, 10877, 16640, 25320, 38735, 58942, 90169, 137209, 209901, 319404, 488618, 743526, 1137433, 1730821, 2647779, 4029100
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.
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
Sequence in context: A093333 A116085 A329692 * A369708 A085570 A059850
KEYWORD
nonn
AUTHOR
Kival Ngaokrajang, Mar 12 2013
EXTENSIONS
a(26) corrected by Bill McEachen, Oct 28 2023
STATUS
approved