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.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• hard
• nice
• more

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

Examples

			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)
		

References

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

Links

• 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, 55-57.

Crossrefs

Cf. A000073, A089047, A133044, A289944.

Extensions

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