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

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).

Links

Table of n, a(n) for n=0..34.

Wikipedia, T-square (fractal)

Kival Ngaokrajang, Illustration for n = 0..4

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

Adjacent sequences: A227618 A227619 A227620 * A227622 A227623 A227624

Keyword

nonn

Author

Kival Ngaokrajang, Jul 17 2013

Status

approved