
COMMENTS

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 + ... + (n1) x_{n1} == 0 (mod n). There is an obvious relation with a(n) since every solution (x_1, ..., x_{n1}) of the linear congruence yields a solution (x_1, ..., x_{n1}; 0, 0, ..., 0, k) of the linear Diophantine equation.


EXAMPLE

The 13 minimal solutions for n=3 are (xcoordinates followed by ycoordinates): (0,0,1;0,0,1), (0,0,1;1,1,0), (0,0,1;3,0,0), (0,0,2;0,3,0), (0,1,0;0,1,0), (0,1,0;2,0,0), (0,2,0;1,0,1), (0,3,0;0,0,2), (1,0,0;1,0,0), (1,0,1;0,2,0), (1,1,0;0,0,1), (2,0,0;0,1,0), (3,0,0;0,0,1).
