

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
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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 1821.
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



