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%I #15 May 09 2023 10:27:12
%S 1,5,5,17,9,29,13,51,28,53,25,115,33,81,73,153,51,176,61,219,121,161,
%T 85,403,126,213,188,353,129,473,145,487,257,335,261,776,201,405,345,
%U 815,243,801,265,731,584,569,313,1407,398,838,559,975,393,1256,573,1375
%N Number of symmetrically distinct sublattices (supercells, superlattices, HNFs) of the tetragonal lattice of index n.
%H Gus L. W. Hart and Rodney W. Forcade, <a href="https://hdl.lib.byu.edu/1877/2951">Algorithm for generating derivative structures</a>, Phys. Rev. B 77, 224115 (2008), <a href="https://doi.org/10.1103/PhysRevB.77.224115">DOI: 10.1103/PhysRevB.77.224115</a> [see Table IV].
%H Materials Simulation Group, <a href="https://github.com/msg-byu/enumlib">Derivative structure enumeration library</a>
%H <a href="/index/Su#sublatts">Index entries for sequences related to sublattices</a>
%o (Python)
%o # see A159842 for the definition of dc, fin, per, u, N, N2
%o def a(n):
%o return (dc(u, N, N2)(n) + 2*dc(fin(1, -1, 0, 4), u, u, N)(n)
%o + 3*dc(fin(1, 3), u, u, N)(n)
%o + 2*dc(fin(1, 1), u, u, per(0, 1, 0, -1))(n)) // 8
%o print([a(n) for n in range(1, 300)])
%o # _Andrey Zabolotskiy_, Jan 31 2020
%Y Cf. A159842, A300782, A300783, A003051, A145393.
%K nonn
%O 1,2
%A _Andrey Zabolotskiy_, Mar 12 2018
%E Terms a(11) and beyond from _Andrey Zabolotskiy_, Jan 31 2020
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