A358715 - OEIS

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.

%I #21 Dec 06 2022 10:00:30

%S 1,2,5,26,220,3622,105859,5677789,553715341,98404068313,

%T 31850967186980,18779046566454536,20167518569123722322,

%U 39451359692134386945019

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

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

%p a(3)=5 because of:

%p /\ /\ /\ /\ /\

%p / \ /\/\ / \ /\/\ /\/\

%p / \ / \/\ /\/\/\ /\/ \ /\/\/\

%Y Cf. A045846, A097076, A358716.

%Y Cf. A290820, A290821, A299705, A300001.

%K nonn,more

%O 1,2

%A _Craig Knecht_ and _John Mason_, Nov 28 2022

%E a(10)-a(14) from _Walter Trump_, Dec 03 2022