OFFSET
0,2
LINKS
Robert P. P. McKone, C++ program to calculate a(n).
Robert P. P. McKone, The distinct Smith normal forms n=1 to n=18.
Robert P. P. McKone, The distinct Smith normal forms n=19 to n=21.
Robert P. P. McKone, The distinct Smith normal forms n=22 to n=23.
Robert P. P. McKone, The distinct Smith normal forms n=24 to n=25.
Robert P. P. McKone, The distinct Smith normal forms n=26.
Robert P. P. McKone, The distinct Smith normal forms n=27.
Robert P. P. McKone, The distinct Smith normal forms n=28.
Robert P. P. McKone, The distinct Smith normal forms n=29.
Robert P. P. McKone, The distinct Smith normal forms n=30.
Robert P. P. McKone, The distinct Smith normal forms n=31.
Eric Weisstein's World of Mathematics, Smith Normal Form.
Wikipedia, Smith normal form
EXAMPLE
The a(2) = 23 diagonals of the Smith normal form matrices are: (0 0 0), (1 0 0), (1 1 0), (1 1 1), (1 1 2), (1 1 3), (1 1 4), (1 1 5), (1 1 6), (1 1 7), (1 1 8), (1 1 9), (1 1 10), (1 2 0), (1 2 2), (1 2 4), (1 2 6), (1 3 0), (1 4 0), (2 0 0), (2 2 0), (2 2 2), (2 2 4).
MATHEMATICA
a[n_]:=a[n]=Length@Union[Diagonal[SmithReduce[Partition[#, 3]]]&/@Tuples[Range[0, n], 9]];
a/@Range[0, 2]
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert P. P. McKone, Apr 12 2026
STATUS
approved
