cp's OEIS Frontend

a(n) is also the number of multisets of integers ranging from 1 to n, such that the sum of the members of the multiset is congruent to 0 mod n, and no submultiset exists whose sum of members is congruent to 0 mod n. These multisets can be thought of as partitions of n in modular arithmetic, thus this sequence can be thought of as a modular arithmetic version of the partition numbers (cf. A000041). - Andrew Weimholt, Jan 31 2011

Every linear Diophantine equation with arbitrary integer coefficients may be reduced to this one.

The minimal nonnegative nonzero solutions form a generating system of the semigroup of all nonnegative solutions.

The asymptotic behavior of a(n) is unknown, it is somewhere between a*exp(b*sqrt(n))/(sqrt(n)) and c*exp(d*n)/n with positive real numbers a,b,c,d.

A096337 contains the number of minimal nonnegative nonzero solutions of the linear congruence x_1 + 2 x_2 + ... + (n-1) x_{n-1} == 0 (mod n). There is an obvious relation with a(n) since every solution (x_1, ..., x_{n-1}) of the linear congruence yields a solution (x_1, ..., x_{n-1}; 0, 0, ..., 0, k) of the linear Diophantine equation.