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A256941 a(n) is the number of free ends of a certain configuration of line segments after n iterations (see Comments lines for definition).

%I A256941 #42 May 26 2021 02:45:32
%S A256941 2,4,8,12,16,24,28,32,32,24,32,48,60,64,68,72,48,24,32,56,88,120,120,
%T A256941 120,104,76,80,120,140,144,148,152,80,24,32,56,88,128,168,224,256,256,
%U A256941 212,216,232,244,224,240,188,92,80,144,232,296,296,296,256,180,176,264,300,304,308,312,144,24
%N A256941 a(n) is the number of free ends of a certain configuration of line segments after n iterations (see Comments lines for definition).
%C A256941 All line segments are equal length. The initial pattern is a straight line segment. It has 2 free ends, so a(0)=2. The construction rules for generation n >= 1 are:
%C A256941 (i) subject to rule ii, add 2 line segments at each free end by arranging in a "V" shape with angle Pi/3 and connecting symmetrically to the free end (nearly like a 3-handed clock showing 07:00:25);
%C A256941 (ii) a "V" is not added if either of its segments would cross a line segment drawn in an earlier generation;
%C A256941 (iii) when generation n is complete, each new line segment clearly touches 2 line segments where it was initially attached; the other end of the new line segment counts as being free if the segment does not touch or cross any more line segments.
%C A256941 a(n) is the number of free ends created in generation n.
%C A256941 It seems that a(n) drops to 24 for n = 5, 9, 17, 33, 65, ... . See illustrations in the links.
%C A256941 The terms of this sequence should be checked! - _Omar E. Pol_, Apr 23 2015
%H A256941 Kival Ngaokrajang, <a href="/A256941/a256941_2.pdf">Illustration of initial terms, n <= 11</a>
%H A256941 Kival Ngaokrajang, <a href="/A256941/a256941_4.pdf">Illustration for a(65) = 24</a>
%Y A256941 Cf. A194270, A194440, A194442, A220500, A220520, A220522, A256641, A256940.
%K A256941 nonn,uned
%O A256941 0,1
%A A256941 _Kival Ngaokrajang_, Apr 19 2015
%E A256941 First term suggested by _Omar E. Pol_, Apr 23 2015
%E A256941 Author's comments edited by _Peter Munn_, May 11 2021