

A300783


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


4



1, 3, 5, 11, 7, 19, 11, 34, 23, 33, 19, 77, 25, 53, 55, 104, 37, 115, 45, 143, 91, 105, 61, 272, 90, 139, 137, 235, 91, 309, 103, 331, 183, 219, 185, 516, 141, 267, 245, 544, 169, 529, 185, 485, 411, 375, 217, 952, 278, 550, 389, 647, 271, 829, 397, 922, 477
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OFFSET

1,2


LINKS

Andrey Zabolotskiy, Table of n, a(n) for n = 1..1000
Gus L. W. Hart and Rodney W. Forcade, Algorithm for generating derivative superstructures, Phys. Rev. B 77, 224115 (2008), DOI: 10.1103/PhysRevB.77.224115 [see Table IV].
Materials Simulation Group, Derivative structure enumeration library
Kohei Shinohara, Atsuto Seko, Takashi Horiyama, Masakazu Ishihata, Junya Honda, Isao Tanaka, Derivative structure enumeration using binary decision diagram, arXiv:2002.12603 [physics.compph], 2020.
Index entries for sequences related to sublattices
Index entries for sequences related to h.c.p. lattice


PROG

(Python)
# see A159842 for the definitions of dc, fin, per, u, N, N2
def a(n):
return (dc(u, N, N2)(n) + 6*dc(fin(1, 1, 0, 4), u, u, N)(n)
+ dc(fin(1, 3), u, u, N)(n)
+ 4*dc(fin(1, 0, 1), u, u, per(0, 1, 1))(n)) // 12
print([a(n) for n in range(1, 100)])
# Andrey Zabolotskiy, Feb 03 2020


CROSSREFS

Cf. A159842, A300782, A300784, A003051, A145393.
Sequence in context: A145398 A087322 A094747 * A287939 A129738 A271314
Adjacent sequences: A300780 A300781 A300782 * A300784 A300785 A300786


KEYWORD

nonn


AUTHOR

Andrey Zabolotskiy, Mar 12 2018


EXTENSIONS

Terms a(11) and beyond from Andrey Zabolotskiy, Feb 03 2020


STATUS

approved



