A014529 - OEIS

%I #62 Feb 23 2018 09:13:33

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

%N 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.

%C 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

%C a(16) is at least 9322. - _Peter Munn_, Feb 20 2018

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

%H Hugo Pfoertner, <a href="/A014529/a014529.txt">Illustrations of configurations for n <= 11</a>

%H Hugo Pfoertner, <a href="/A014529/a014529_1.txt">Illustration of configuration for n = 12</a>, based on personal communication from _Peter Munn_

%H Hugo Pfoertner, <a href="/A014529/a014529_2.txt">Illustration of configuration for n = 13</a>, based on data in A289944 from _Peter Munn_

%H Rainer Rosenthal, <a href="/A014529/a014529.gif">Illustration of configuration for n = 14</a>, based on description in A289944 from _Peter Munn_

%H Rainer Rosenthal, <a href="/A014529/a014529_1.gif">Illustration of configuration for n = 15</a>, based on description in A289944 from _Peter Munn_

%H Ian Stewart, <a href="http://www.spektrum.de/magazin/die-unscheinbare-schwester-der-goldenen-zahl/824251">Die unscheinbare Schwester der goldenen Zahl</a>, Spektrum der Wissenschaft, Dossier 02/2003: Mathematische Unterhaltungen II, 55-57.

%e From _Peter Kagey_, Jul 31 2017: (Start)

%e For n = 6 a convex polygon with area 20 is:

%e       *-------*

%e      / \     / \

%e     /   \   /   \

%e    /     \ /     \

%e   *---*---*       \

%e    \ / \ /         \

%e     *---*-----------*

%e The sides are relatively prime because gcd(1, 1, 1, 2, 2, 3) = 1. (End)

%Y Cf. A000073, A089047, A133044, A289944.

%K nonn,hard,nice,more

%O 1,2

%A _N. J. A. Sloane_

%E Terms a(12)-a(15) from _John W. Layman_