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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, 387735, 58942, 90169, 137209, 209901, 319404, 488618, 743526, 1137433, 1730821, 2647779, 4029100 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..37.

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

Sequence in context: A093335 A093333 A116085 * A085570 A059850 A308906

Adjacent sequences:  A216195 A216196 A216197 * A216199 A216200 A216201

KEYWORD

nonn

AUTHOR

Kival Ngaokrajang, Mar 12 2013

STATUS

approved

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Last modified August 18 08:57 EDT 2019. Contains 326077 sequences. (Running on oeis4.)