A061289 - OEIS

%I #12 Jul 07 2023 14:39:49

%S 3,7,10,14,17

%N Consider a network of triangles consisting of an equilateral triangle divided into n^2 equilateral triangles plus a circle connecting the vertices of the main triangle. Sequence gives minimal number of corner turns required to trace the network in one continuous line.

%D Martin Gardner, More Mathematical Puzzles and Diversions, page 63, "a network tracing puzzle".

%e a(1)=3 since you have to make two turns to trace the triangle and one to cover the circular part of the network.

%e From _Sean A. Irvine_, Feb 07 2023: (Start)

%e a(3)=10, there are 9 triangles:

%e           A

%e          / \

%e         B---C

%e        / \ / \

%e       D---E---F

%e      / \ / \ / \

%e     G---H---I---J

%e Start on the circle (which passes through A, G, J, but is not shown in this picture), then trace the complete figure with A-J-G-B-I-F-D-H-C-B-A for a total of 10 turns. Note other paths achieving the same minimum number of turns are possible. (End)

%K nonn,hard,more

%O 1,1

%A Brian Wallace (wallacebrianedward(AT)yahoo.co.uk), May 22 2001

%E a(3) onward corrected by _Sean A. Irvine_, Feb 07 2023