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A061289
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.
0
3, 7, 10, 14, 17
OFFSET
1,1
REFERENCES
Martin Gardner, More Mathematical Puzzles and Diversions, page 63, "a network tracing puzzle".
EXAMPLE
a(1)=3 since you have to make two turns to trace the triangle and one to cover the circular part of the network.
From Sean A. Irvine, Feb 07 2023: (Start)
a(3)=10, there are 9 triangles:
A
/ \
B---C
/ \ / \
D---E---F
/ \ / \ / \
G---H---I---J
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)
CROSSREFS
Sequence in context: A289114 A289027 A027704 * A288999 A310187 A198268
KEYWORD
nonn,hard,more
AUTHOR
Brian Wallace (wallacebrianedward(AT)yahoo.co.uk), May 22 2001
EXTENSIONS
a(3) onward corrected by Sean A. Irvine, Feb 07 2023
STATUS
approved