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A300784 Number of symmetrically distinct sublattices (supercells, superlattices, HNFs) of the tetragonal lattice of index n. 3
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 (list; graph; refs; listen; history; text; internal format)
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 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

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

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Last modified July 30 17:21 EDT 2021. Contains 346359 sequences. (Running on oeis4.)