A300782 Number of symmetrically distinct sublattices (supercells, superlattices, HNFs) of the simple cubic lattice of index n.

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

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 structures, 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