This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A300784 #15 May 09 2023 10:27:12 %S A300784 1,5,5,17,9,29,13,51,28,53,25,115,33,81,73,153,51,176,61,219,121,161, %T A300784 85,403,126,213,188,353,129,473,145,487,257,335,261,776,201,405,345, %U A300784 815,243,801,265,731,584,569,313,1407,398,838,559,975,393,1256,573,1375 %N A300784 Number of symmetrically distinct sublattices (supercells, superlattices, HNFs) of the tetragonal lattice of index n. %H A300784 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 A300784 Materials Simulation Group, <a href="https://github.com/msg-byu/enumlib">Derivative structure enumeration library</a> %H A300784 <a href="/index/Su#sublatts">Index entries for sequences related to sublattices</a> %o A300784 (Python) %o A300784 # see A159842 for the definition of dc, fin, per, u, N, N2 %o A300784 def a(n): %o A300784 return (dc(u, N, N2)(n) + 2*dc(fin(1, -1, 0, 4), u, u, N)(n) %o A300784 + 3*dc(fin(1, 3), u, u, N)(n) %o A300784 + 2*dc(fin(1, 1), u, u, per(0, 1, 0, -1))(n)) // 8 %o A300784 print([a(n) for n in range(1, 300)]) %o A300784 # _Andrey Zabolotskiy_, Jan 31 2020 %Y A300784 Cf. A159842, A300782, A300783, A003051, A145393. %K A300784 nonn %O A300784 1,2 %A A300784 _Andrey Zabolotskiy_, Mar 12 2018 %E A300784 Terms a(11) and beyond from _Andrey Zabolotskiy_, Jan 31 2020