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A227621
The nearest integer of perimeter of T-square (fractal) after n-iterations, starting with a unit square.
1
4, 8, 14, 23, 37, 57, 87, 133, 201, 304, 457, 688, 1034, 1553, 2331, 3499, 5251, 7878, 11819, 17731, 26598, 39899, 59851, 89778, 134669, 202005, 303010, 454517, 681778, 1022668, 1534004, 2301009, 3451515, 5177275, 7765914
OFFSET
0,1
COMMENTS
The round (nearest) function uses the convention that values halfway between two integers are rounded up, so a(4) = 37 = round(36 + 1/2).
FORMULA
a(0) = 4; for n >= 1, a(n) = round(A083313(n)/2^(n-3)).
EXAMPLE
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.
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.
MAPLE
A227621 := proc(n)
if n = 0 then 4
else
round(A083313(n)/2^(n-3)) ;
end if;
end proc: # R. J. Mathar, Aug 01 2013
PROG
(Small Basic)
a[0]=4
For n = 0 To 51
a[n+1] = Math.Round((Math.Power(3, n+1) - Math.Power(2, n))/Math.Power(2, n-2))
TextWindow.Write(a[n]+", ")
EndFor
CROSSREFS
Cf. A083313.
Sequence in context: A193711 A079328 A073612 * A060064 A374338 A045474
KEYWORD
nonn
AUTHOR
Kival Ngaokrajang, Jul 17 2013
STATUS
approved