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%I #29 May 09 2023 10:27:01
%S 1,3,5,11,7,19,11,34,23,33,19,77,25,53,55,104,37,115,45,143,91,105,61,
%T 272,90,139,137,235,91,309,103,331,183,219,185,516,141,267,245,544,
%U 169,529,185,485,411,375,217,952,278,550,389,647,271,829,397,922,477
%N Number of symmetrically distinct sublattices (supercells, superlattices, HNFs) of the 3D hexagonal lattice of index n.
%H Andrey Zabolotskiy, <a href="/A300783/b300783.txt">Table of n, a(n) for n = 1..1000</a>
%H Gus L. W. Hart and Rodney W. Forcade, <a href="https://hdl.lib.byu.edu/1877/2951">Algorithm for generating derivative structures</a>, Phys. Rev. B 77, 224115 (2008), <a href="https://doi.org/10.1103/PhysRevB.77.224115">DOI: 10.1103/PhysRevB.77.224115</a> [see Table IV].
%H Materials Simulation Group, <a href="https://github.com/msg-byu/enumlib">Derivative structure enumeration library</a>
%H Kohei Shinohara, Atsuto Seko, Takashi Horiyama, Masakazu Ishihata, Junya Honda and Isao Tanaka, <a href="https://doi.org/10.1063/5.0021663">Enumeration of nonequivalent substitutional structures using advanced data structure of binary decision diagram</a>, J. Chem. Phys. 153, 104109 (2020); preprint: <a href="https://arxiv.org/abs/2002.12603">Derivative structure enumeration using binary decision diagram</a>, arXiv:2002.12603 [physics.comp-ph], 2020.
%H <a href="/index/Su#sublatts">Index entries for sequences related to sublattices</a>
%o (Python)
%o # see A159842 for the definitions of dc, fin, per, u, N, N2
%o def a(n):
%o return (dc(u, N, N2)(n) + 6*dc(fin(1, -1, 0, 4), u, u, N)(n)
%o + dc(fin(1, 3), u, u, N)(n)
%o + 4*dc(fin(1, 0, 1), u, u, per(0, 1, -1))(n)) // 12
%o print([a(n) for n in range(1, 100)])
%o # _Andrey Zabolotskiy_, Feb 03 2020
%Y Cf. A159842, A300782, A300784, A003051, A145393.
%K nonn
%O 1,2
%A _Andrey Zabolotskiy_, Mar 12 2018
%E Terms a(11) and beyond from _Andrey Zabolotskiy_, Feb 03 2020
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