A256156 Triangular array of numbers of 2-polymatroids of rank k on n unlabeled points, for n>=0, 0<=k<=2n.

1, 1, 1, 1, 1, 2, 4, 2, 1, 1, 3, 10, 12, 10, 3, 1, 1, 4, 21, 49, 78, 49, 21, 4, 1, 1, 5, 39, 172, 584, 778, 584, 172, 39, 5, 1, 1, 6, 68, 573, 5236, 18033, 46661, 18033, 5236, 573, 68, 6, 1, 1, 7, 112, 1890, 72205, 971573, 149636721, 19498369, 149636721, 971573, 72205, 1890, 112, 7, 1

Offset: 0

Author

Max Alekseyev, Mar 16 2015

Keywords

• nonn
• tabf

Comments

The rows are symmetric: a(n,k) = a(n,2n-k).

Starting with n=7, the rows are not unimodal.

Examples

			Triangle starts with:
n=0: 1
n=1: 1 1 1
n=2: 1 2 4 2 1
n=3: 1 3 10 12 10 3 1
n=4: 1 4 21 49 78 49 21 4 1
n=5: 1 5 39 172 584 778 584 172 39 5 1
n=6: 1 6 68 573 5236 18033 46661 18033 5236 573 68 6 1
n=7: 1 7 112 1890 72205 971573 149636721 19498369 149636721 971573 72205 1890 112 7 1
		

Links

• Thomas J. Savitsky, Enumeration of 2-polymatroids on up to seven elements. SIAM J. Discrete Math., 28(4):1641-1650, 2014. arXiv:1401.8006

Crossrefs

Cf. A256157, A256158, A256159, A053534