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

2, 4, 8, 12, 16, 24, 28, 32, 32, 24, 32, 48, 60, 64, 68, 72, 48, 24, 32, 56, 88, 120, 120, 120, 104, 76, 80, 120, 140, 144, 148, 152, 80, 24, 32, 56, 88, 128, 168, 224, 256, 256, 212, 216, 232, 244, 224, 240, 188, 92, 80, 144, 232, 296, 296, 296, 256, 180, 176, 264, 300, 304, 308, 312, 144, 24

Offset

0,1

Comments

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:

(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);

(ii) a "V" is not added if either of its segments would cross a line segment drawn in an earlier generation;

(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.

a(n) is the number of free ends created in generation n.

It seems that a(n) drops to 24 for n = 5, 9, 17, 33, 65, ... . See illustrations in the links.

The terms of this sequence should be checked! - Omar E. Pol, Apr 23 2015

Links

Table of n, a(n) for n=0..65.

Kival Ngaokrajang, Illustration of initial terms, n <= 11

Kival Ngaokrajang, Illustration for a(65) = 24

Crossrefs

Cf. A194270, A194440, A194442, A220500, A220520, A220522, A256641, A256940.

Sequence in context: A308013 A260090 A351873 * A324174 A047836 A325762

Adjacent sequences: A256938 A256939 A256940 * A256942 A256943 A256944

Keyword

nonn,uned

Author

Kival Ngaokrajang, Apr 19 2015

Extensions

First term suggested by Omar E. Pol, Apr 23 2015

Author's comments edited by Peter Munn, May 11 2021

Status

approved