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A300783 Number of symmetrically distinct sublattices (supercells, superlattices, HNFs) of the 3D hexagonal lattice of index n. 4


%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 superstructures</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, Isao Tanaka, <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>

%H <a href="/index/Ha#hcp">Index entries for sequences related to h.c.p. lattice</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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Last modified July 30 17:21 EDT 2021. Contains 346359 sequences. (Running on oeis4.)