A300784 Number of symmetrically distinct sublattices (supercells, superlattices, HNFs) of the tetragonal lattice of index n.

1, 5, 5, 17, 9, 29, 13, 51, 28, 53, 25, 115, 33, 81, 73, 153, 51, 176, 61, 219, 121, 161, 85, 403, 126, 213, 188, 353, 129, 473, 145, 487, 257, 335, 261, 776, 201, 405, 345, 815, 243, 801, 265, 731, 584, 569, 313, 1407, 398, 838, 559, 975, 393, 1256, 573, 1375

Offset: 1

Author

Andrey Zabolotskiy, Mar 12 2018

Keywords

• nonn

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
• Index entries for sequences related to sublattices

Crossrefs

Cf. A159842, A300782, A300783, A003051, A145393.

Programs

Python

# see A159842 for the definition of dc, fin, per, u, N, N2
def a(n):
    return (dc(u, N, N2)(n) + 2*dc(fin(1, -1, 0, 4), u, u, N)(n)
      + 3*dc(fin(1, 3), u, u, N)(n)
      + 2*dc(fin(1, 1), u, u, per(0, 1, 0, -1))(n)) // 8
print([a(n) for n in range(1, 300)])
# Andrey Zabolotskiy, Jan 31 2020

Extensions

Terms a(11) and beyond from Andrey Zabolotskiy, Jan 31 2020