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%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
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