OFFSET
1,2
COMMENTS
Consider the set of 3 x 3 matrices with integer entries of a fixed determinant n. The group GL(3, \Z) acts on the right by multiplication. Similarly, the symmetric group S_3 acts on the left via multiplication by permutation matrices. The entry a_n is the number of elements in the double orbit space S_3\det^{-1}(n)/GL(3,\Z). The sequence a_n also gives the number of isomorphism classes of simplicial cones in \Z^3 of a certain index, or alternatively the number of affine toric varieties in dimension 3 arising from simplicial cones.
LINKS
Atanas Atanasov, Table of n, a(n) for n=1..210
EXAMPLE
For n = 2, two orbit representatives are ((1,0,0),(0,1,0),(0,1,2)) and ((1,0,0),(0,1,0),(1,1,2)). For n = 3, we have ((1,0,0),(0,1,0),(0,1,3)), ((1,0,0),(0,1,0),(0,2,3)), ((1,0,0),(0,1,0),(1,1,3)) and ((1,0,0),(0,1,0),(2,2,3)).
CROSSREFS
KEYWORD
nonn
AUTHOR
Atanas Atanasov (ava2102(AT)columbia.edu), Jun 26 2009
EXTENSIONS
Terms a(24) and beyond from b-file by Andrew Howroyd, Feb 05 2018
STATUS
approved