OFFSET
0,3
COMMENTS
This is the number of ways of writing the vector 2*rho = (n,n-2,...,-n+2,-n) as a sum of the vectors e_i - e_j for 1 <= i < j <= n+1 with nonnegative integer coefficients. - Alejandro H. Morales, May 24 2024
LINKS
FORMULA
See MathOverflow link for a recurrence.
EXAMPLE
For n = 2, the a(2) = 3 solutions are
0*(1, -1, 0) + 2*(1, 0, -1) + 0*(0, 1, -1) = (2, 0, -2),
1*(1, -1, 0) + 1*(1, 0, -1) + 1*(0, 1, -1) = (2, 0, -2),
2*(1, -1, 0) + 0*(1, 0, -1) + 2*(0, 1, -1) = (2, 0, -2).
MAPLE
multcoeff:=proc(n, f, coeffv, k)
local i, currcoeff;
currcoeff:=f;
for i from 1 to n do
currcoeff:=`if`(coeffv[i]=0, coeff(series(currcoeff, x[i], k), x[i], 0), coeff(series(currcoeff, x[i], k), x[i]^coeffv[i]));
end do;
return currcoeff; end proc:F:=n->mul(mul((1-x[i]*x[j]^(-1))^(-1), j=i+1..n), i=1..n):
a := n -> multcoeff(n+1, F(n+1), [seq(n-2*i, i=0..n)], 2*n):
seq(a(i), i=0..5) # Alejandro H. Morales, May 24 2024
CROSSREFS
KEYWORD
nonn,more
AUTHOR
N. J. A. Sloane, Jul 30 2012
EXTENSIONS
a(0) and a(7)-a(9) from Alejandro H. Morales, May 24 2024
STATUS
approved