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

Author

Kival Ngaokrajang, Jul 17 2013

Keywords

• nonn

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).

Examples

			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.
		

Links

• Wikipedia, T-square (fractal)
• Kival Ngaokrajang, Illustration for n = 0..4

Crossrefs

Cf. A083313.

Programs

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

Formula

a(0) = 4; for n >= 1, a(n) = round(A083313(n)/2^(n-3)).