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

1,2

Links

Table of n, a(n) for n=1..56.

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

Prog

(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

Crossrefs

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

Sequence in context: A253065 A294612 A246332 * A273326 A273421 A273758

Adjacent sequences: A300781 A300782 A300783 * A300785 A300786 A300787

Keyword

nonn

Author

Andrey Zabolotskiy, Mar 12 2018

Extensions

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

Status

approved