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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
OFFSET
1,2
LINKS
Gus L. W. Hart and Rodney W. Forcade, Algorithm for generating derivative structures, 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 and Isao Tanaka, Enumeration of nonequivalent substitutional structures using advanced data structure of binary decision diagram, J. Chem. Phys. 153, 104109 (2020); preprint: Derivative structure enumeration using binary decision diagram, arXiv:2002.12603 [physics.comp-ph], 2020.
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
KEYWORD
nonn
AUTHOR
Andrey Zabolotskiy, Mar 12 2018
EXTENSIONS
Terms a(11) and beyond from Andrey Zabolotskiy, Feb 03 2020
STATUS
approved