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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 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.)