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A256940 a(n) is the total number of free ends of a certain configuration of line segments after n iterations (see Comments lines for definition). 2

%I

%S 2,4,8,12,12,12,20,20,16,24,28,48,52,36,44,36,16,24,40,56,72,72,76,80,

%T 60,64,80,120,132,88,100,68,16,24,40,56,72,80,88,104,112,128,176,216,

%U 244,212,168,148,84,64,104,152,200,200,212,216,148,144,176,276,292,192,212,132,16

%N a(n) is the total number of free ends of a certain configuration of line segments after n iterations (see Comments lines for definition).

%C The initial pattern is a straight line segment which has 2 free ends: a(0)=2.

%C The construction rules for the following generations are:

%C (i) add 2 line segments (all line segments are of equal length) at each free end of previous generation by arranging them in a "V" shape at angle Pi/2 and symmetrically placed at the free end,

%C (ii) overlaps among different generations are prohibited,

%C (iii) the {a(n)} free ends are the ends of elements that do not toucht or cross the others.

%C It seems that a(n) drop to 16 for n = 8, 16, 32, 64,... . See illustration in the links.

%C The structure of the illustration of initial terms is very similar to the structure of A194270 and A220500. The terms of this sequence should be checked! - _Omar E. Pol_, Apr 19 2015

%H Kival Ngaokrajang, <a href="/A256940/a256940_2.pdf">Illustration of initial terms, n <= 12</a>

%H Kival Ngaokrajang, <a href="/A256940/a256940_3.pdf">Illustration for a(64)=16</a>

%Y Cf. A194270, A194440, A194442, A220500, A220520, A220522, A256641, A256941.

%K nonn

%O 0,1

%A _Kival Ngaokrajang_, Apr 19 2015

%E a(1) = 2 prepended and a(3) = 8 corrected by _Omar E. Pol_, Apr 19 2015

%E Partially edited by _Kival Ngaokrajang_, as _Omar E. Pol_ suggestion, Apr 26 2015

%E Terms a(12), a(13), a(59) corrected by _Kival Ngaokrajang_, Apr 26 2015

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Last modified July 13 13:48 EDT 2020. Contains 335688 sequences. (Running on oeis4.)