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A227621 The nearest integer of perimeter of T-square (fractal) after n-iterations, starting with a unit square.

%I A227621 #19 Dec 12 2015 13:15:09
%S A227621 4,8,14,23,37,57,87,133,201,304,457,688,1034,1553,2331,3499,5251,7878,
%T A227621 11819,17731,26598,39899,59851,89778,134669,202005,303010,454517,
%U A227621 681778,1022668,1534004,2301009,3451515,5177275,7765914
%N A227621 The nearest integer of perimeter of T-square (fractal) after n-iterations, starting with a unit square.
%C A227621 The round (nearest) function uses the convention that values halfway between two integers are rounded up, so a(4) = 37 = round(36 + 1/2).
%H A227621 Wikipedia, <a href="http://en.wikipedia.org/wiki/T-square_(fractal)">T-square (fractal)</a>
%H A227621 Kival Ngaokrajang, <a href="/A227621/a227621.jpg">Illustration for n = 0..4</a>
%F A227621 a(0) = 4; for n >= 1, a(n) = round(A083313(n)/2^(n-3)).
%e A227621 The central unit square has perimeter 4. At n=1, the additional 4 squares hide 4*1/2 = 2 units of length and add 4*3*1/2 = 6 units, to give a(1) = 4 - 2 + 6 = 8.
%e A227621 At n=2, the additional 12 squares hide 12*1/(2*2) units of length and add 12*3*1/(2*2) to give a(2) = 8 - 12/4 + 36/4 = 14.
%p A227621 A227621 := proc(n)
%p A227621     if n = 0 then 4
%p A227621     else
%p A227621         round(A083313(n)/2^(n-3)) ;
%p A227621     end if;
%p A227621 end proc: # _R. J. Mathar_, Aug 01 2013
%o A227621 (Small Basic)
%o A227621 a[0]=4
%o A227621 For n = 0 To 51
%o A227621   a[n+1] = Math.Round((Math.Power(3,n+1) - Math.Power(2,n))/Math.Power(2,n-2))
%o A227621   TextWindow.Write(a[n]+", ")
%o A227621 EndFor
%Y A227621 Cf. A083313.
%K A227621 nonn
%O A227621 0,1
%A A227621 _Kival Ngaokrajang_, Jul 17 2013