A061289 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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:

/ \

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