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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 (list; graph; refs; listen; history; text; internal format)
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.comp-ph], 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

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Last modified June 14 09:06 EDT 2021. Contains 345018 sequences. (Running on oeis4.)