A358715 a(n) is the number of distinct ways to cut an equilateral triangle with edges of size n into equilateral triangles with integer sides.

1, 2, 5, 26, 220, 3622, 105859, 5677789, 553715341, 98404068313, 31850967186980, 18779046566454536, 20167518569123722322, 39451359692134386945019

Offset

1,2

Comments

In other words, the number of equilateral triangular tilings of an equilateral triangle, where rotations and reflections are considered distinct.

Links

Table of n, a(n) for n=1..14.

Maple

a(3)=5 because of:
    /\      /\      /\      /\      /\
   /  \    /\/\    /  \    /\/\    /\/\
  /    \  /  \/\  /\/\/\  /\/  \  /\/\/\

Crossrefs

Cf. A045846, A097076, A358716.

Cf. A290820, A290821, A299705, A300001.

Sequence in context: A072268 A019014 A128595 * A180749 A323299 A111195

Adjacent sequences: A358712 A358713 A358714 * A358716 A358717 A358718

Keyword

nonn,more

Author

Craig Knecht and John Mason, Nov 28 2022

Extensions

a(10)-a(14) from Walter Trump, Dec 03 2022

Status

approved