

A014529


Largest convex area that can be tiled with n equilateral triangles whose sides s_k are relatively prime, i.e., gcd(s_1,...,s_n) = 1.


6



1, 2, 3, 7, 11, 20, 36, 71, 146, 260, 495, 860, 1559, 2831, 5114
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OFFSET

1,2


COMMENTS

The terms published to date (n <= 15) are consistent with a tribonacci growth rate. Specifically, floor(A000073(n+2) * 5/6) <= a(n) <= A000073(n+2).  Peter Munn, Sep 27 2017
a(16) is at least 9322.  Peter Munn, Feb 20 2018


REFERENCES

Robert T. Wainwright, quoted by Ian Stewart, Math. Recreations, Scientific American, Jul 15 1997, p. 96.


LINKS

Table of n, a(n) for n=1..15.
Hugo Pfoertner, Illustrations of configurations for n <= 11
Hugo Pfoertner, Illustration of configuration for n = 12, based on personal communication from Peter Munn
Hugo Pfoertner, Illustration of configuration for n = 13, based on data in A289944 from Peter Munn
Rainer Rosenthal, Illustration of configuration for n = 14, based on description in A289944 from Peter Munn
Rainer Rosenthal, Illustration of configuration for n = 15, based on description in A289944 from Peter Munn
Ian Stewart, Die unscheinbare Schwester der goldenen Zahl, Spektrum der Wissenschaft, Dossier 02/2003: Mathematische Unterhaltungen II, 5557.


EXAMPLE

From Peter Kagey, Jul 31 2017: (Start)
For n = 6 a convex polygon with area 20 is:
**
/ \ / \
/ \ / \
/ \ / \
*** \
\ / \ / \
***
The sides are relatively prime because gcd(1, 1, 1, 2, 2, 3) = 1. (End)


CROSSREFS

Cf. A000073, A089047, A133044, A289944.
Sequence in context: A245738 A265093 A133044 * A095015 A024367 A232432
Adjacent sequences: A014526 A014527 A014528 * A014530 A014531 A014532


KEYWORD

nonn,hard,nice,more


AUTHOR

N. J. A. Sloane


EXTENSIONS

Terms a(12)a(15) from John W. Layman


STATUS

approved



