OFFSET
1,5
LINKS
J. L. Martin, The slopes determined by n points in the plane.
Martin, Jeremy L. The slopes determined by n points in the plane. Duke Math. J. 131 (2006), no. 1, 119-165 (also arXiv math.AG/0302106, but beware errors).
FORMULA
Recurrence: d(n, k) = 1 for n=0 or k=1, d(n, k) = 0 for n>0 and either k<0 or k>n, d(n, k) = d(n-1, k) + d(n, k-1) + sum( binomial(k-1, w)*binomial(n-k, x)*d(n-k+w-x, w+1)*d(k-w+x, k-w-1), w=0..k-2, x=0..n-k-1)
EXAMPLE
Triangle begins
1,
1, 1,
1, 3, 3,
1, 7, 15, 15,
1, 15, 57, 105, 105,
1, 31, 195, 561, 945, 945,
1, 63, 633, 2685, 6555, 10395, 10395,
...
CROSSREFS
KEYWORD
AUTHOR
Jeremy Martin (martin(AT)math.umn.edu), Feb 05 2003
STATUS
approved