cp's OEIS Frontend

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 A358715 #23 May 10 2025 16:16:01
%S A358715 1,2,5,26,220,3622,105859,5677789,553715341,98404068313,
%T A358715 31850967186980,18779046566454536,20167518569123722322,
%U A358715 39451359692134386945019
%N 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.
%C A358715 In other words, the number of equilateral triangular tilings of an equilateral triangle, where rotations and reflections are considered distinct.
%e A358715 a(3)=5 because of:
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%e A358715    /  \    /\/\    /  \    /\/\    /\/\
%e A358715   /    \  /  \/\  /\/\/\  /\/  \  /\/\/\
%Y A358715 Cf. A045846, A097076, A358716.
%Y A358715 Cf. A290820, A290821, A299705, A300001.
%K A358715 nonn,more
%O A358715 1,2
%A A358715 _Craig Knecht_ and _John Mason_, Nov 28 2022
%E A358715 a(10)-a(14) from _Walter Trump_, Dec 03 2022