%I #12 Apr 05 2024 19:46:51
%S 2,3,6,14,36,94,250,675,1832,5005,13746,37901,104902,291312,811346,
%T 2265905,6343854,17801383,50057400,141034248,398070362,1125426581,
%U 3186725646,9036406687,25658313188,72946289247,207628101578,591622990214,1687527542874,4818113792640
%N Number of fixed polyiamonds of area n without holes.
%C Equivalently, closed self-avoiding paths on the hexagonal net, where rotations and reflections of the whole path are not allowed and there is no selected starting point, with enclosed area n.
%H Andrey Zabolotskiy, <a href="/A341630/b341630.txt">Table of n, a(n) for n = 1..60</a> (from Iwan Jensen's table)
%H Anthony J. Guttmann, editor, <a href="https://doi.org/10.1007/978-1-4020-9927-4">Polygons, Polyominoes and Polycubes</a>, LNP 775, Springer, 2009. See Table 16.8 "Triangular lattice SAP by area" on p. 476 with reference "Iwan Jensen, Unpublished".
%H <a href="/index/Aa#A2">Index entries for sequences related to A2 = hexagonal = triangular lattice</a>
%Y Cf. A001420 (polyiamonds with holes allowed; first deviates at n=9), A036418 (polyiamonds with given perimeter, i.e. paths with given length), A070765 (free polyiamonds, i.e. reduced for symmetry: rotations and reflections are allowed), A006724 (analog for square lattice).
%K nonn
%O 1,1
%A _Andrey Zabolotskiy_, Feb 16 2021