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A300782
Number of symmetrically distinct sublattices (supercells, superlattices, HNFs) of the simple cubic lattice of index n.
4
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
OFFSET
1,2
PROG
(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
KEYWORD
nonn
AUTHOR
Andrey Zabolotskiy, Mar 12 2018
EXTENSIONS
Terms a(11) and beyond from Andrey Zabolotskiy, Sep 02 2019
STATUS
approved