%I #28 Nov 29 2023 13:07:19
%S 0,0,1,1,1,4,5,16,37,120,344,1175,3807,13224,45645,161705,575325,
%T 2074088,7521818,27502445,101134999,374128188
%N Number of n-step 2-dimensional closed self-avoiding paths on triangular lattice, reduced for symmetry, i.e., where rotations and reflections are not counted as distinct.
%C Differs from A057729 beginning at n = 11, since that sequence includes triangular polyominoes with holes.
%C a(n) is the number of simply connected polyiamonds with perimeter n. - _Walter Trump_, Nov 29 2023
%H Rade Doroslovački, Ivan Stojmenović and Ratko Tošić, <a href="https://doi.org/10.1007/BF01937351">Generating and counting triangular systems</a>, BIT Numerical Mathematics, 27 (1987), 18-24. See Table 1.
%H Hugo Pfoertner, <a href="https://oeis.org/plot2a?name1=A036418&name2=A284869&tform1=untransformed&tform2=untransformed&shift=0&radiop1=ratio&drawpoints=true">Illustration of ratio A036418(n)/a(n) using Plot2</a>.
%H Hugo Pfoertner, <a href="http://www.randomwalk.de/sequences/a284869.htm">Illustration of polygons of perimeter <= 11</a>.
%H Walter Trump, <a href="/A284869/a284869.pdf">Self-avoiding closed walks on a triangular lattice</a>
%Y Approaches (1/12)*A036418 for increasing n.
%Y Cf. A057729, A258206, A266549, A316196.
%K nonn,walk,more
%O 1,6
%A _Luca Petrone_, Apr 04 2017
%E a(15) from _Hugo Pfoertner_, Jun 27 2018
%E a(16)-a(22) from _Walter Trump_, Nov 29 2023