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Gus L. W. Hart and Rodney W. Forcade, <a href="https://scholarsarchive.byu.edu/facpub/180/">Algorithm for generating derivative superstructuresstructures</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].

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Gus L. W. Hart and Rodney W. Forcade, <a href="httphttps://msgscholarsarchive.byu.edu/papersfacpub/180/GLWHart_enumeration.pdf">Algorithm for generating derivative superstructures</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].

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proposed

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Cf. A159842, A300783, A300784, A003051, A145393, A001001, A128119, A160870, A145396, A145398.

Andrey Zabolotskiy, <a href="/A300782/b300782.txt">Table of n, a(n) for n = 1..1000</a>

Matt DeCross, <a href="https://mdecross.github.io/LatticePolytopesandOrbifolds.pdf">Lattice Polytopes and Orbifolds</a>, 2015.

1, 3, 3, 9, 5, 13, 7, 24, 14, 23, 11, 49, 15, 33, 31, 66, 21, 70, 25, 89, 49, 61, 33, 162, 50, 81, 75, 137, 49, 177, 55, 193, 97, 123, 99, 296, 75, 147, 129, 312, 89, 291, 97, 269, 218, 203, 113, 534, 146, 302, 203, 357, 141, 451, 207, 508, 247, 307, 171, 789

Matt DeCross, <a href="https://mdecross.github.io/OrbifoldsTalk.pdf">Lattice Polytopes and Orbifolds in Quiver Gauge Theories</a>, 2015. See slides 18-21.

(Python)

# see A159842 for the definition of dc, fin, per, u, N, N2

def a(n): # from DeCross's slides

return (dc(u, N, N2)(n) + 6*dc(fin(1, -1, 0, 4), u, u, N)(n)

+ 3*dc(fin(1, 3), u, u, N)(n)

+ 8*dc(fin(1, 0, -1, 0, 0, 0, 0, 0, 3), u, u, per(0, 1, -1))(n)

+ 6*dc(fin(1, 1), u, u, per(0, 1, 0, -1))(n))//24

print([a(n) for n in range(1, 300)])

# Andrey Zabolotskiy, Sep 02 2019

nonn,more

nonn

Terms a(11) and beyond from Andrey Zabolotskiy, Sep 02 2019

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