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A300782 Number of symmetrically distinct sublattices (supercells, superlattices, HNFs) of the simple cubic lattice of index n. 4
1, 3, 3, 9, 5, 13, 7, 24, 14, 23, 11, 49, 15, 33, 31, 66, 21, 70, 25, 89, 49, 61, 33, 162, 50, 81, 75, 137, 49, 177, 55, 193, 97, 123, 99, 296, 75, 147, 129, 312, 89, 291, 97, 269, 218, 203, 113, 534, 146, 302, 203, 357, 141, 451, 207, 508, 247, 307, 171, 789 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Andrey Zabolotskiy, Table of n, a(n) for n = 1..1000

Matt DeCross, Lattice Polytopes and Orbifolds, 2015.

Matt DeCross, Lattice Polytopes and Orbifolds in Quiver Gauge Theories, 2015. See slides 18-21.

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

Index entries for sequences related to sublattices

Index entries for sequences related to cubic lattice

PROG

(Python)

# see A159842 for the definition of dc, fin, per, u, N, N2

def a(n): # from DeCross's slides

    return (dc(u, N, N2)(n) + 6*dc(fin(1, -1, 0, 4), u, u, N)(n)

      + 3*dc(fin(1, 3), u, u, N)(n)

      + 8*dc(fin(1, 0, -1, 0, 0, 0, 0, 0, 3), u, u, per(0, 1, -1))(n)

      + 6*dc(fin(1, 1), u, u, per(0, 1, 0, -1))(n))//24

print([a(n) for n in range(1, 300)])

# Andrey Zabolotskiy, Sep 02 2019

CROSSREFS

Cf. A159842, A300783, A300784, A003051, A145393, A001001, A128119, A160870, A145396, A145398.

Sequence in context: A066572 A307379 A276147 * A104195 A294178 A062131

Adjacent sequences:  A300779 A300780 A300781 * A300783 A300784 A300785

KEYWORD

nonn

AUTHOR

Andrey Zabolotskiy, Mar 12 2018

EXTENSIONS

Terms a(11) and beyond from Andrey Zabolotskiy, Sep 02 2019

STATUS

approved

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Last modified August 3 21:19 EDT 2021. Contains 346441 sequences. (Running on oeis4.)