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.

3, 7, 10, 14, 17

Offset

1,1

References

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

Links

Table of n, a(n) for n=1..5.

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

Adjacent sequences: A061286 A061287 A061288 * A061290 A061291 A061292

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