A256158 Triangular array of numbers of 2-polymatroids of rank k on n labeled points, for n>=0, 0<=k<=2n.

1, 1, 1, 1, 1, 3, 6, 3, 1, 1, 7, 29, 41, 29, 7, 1, 1, 15, 135, 477, 784, 477, 135, 15, 1, 1, 31, 642, 5957, 27375, 41695, 27375, 5957, 642, 31, 1, 1, 63, 3199, 87477, 1554077, 7109189, 21937982, 7109189, 1554077, 87477, 3199, 63, 1, 1, 127, 16879, 1604768, 189213842, 3559635761, 733133160992, 86322358307, 733133160992, 3559635761, 189213842, 1604768, 16879, 127, 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 3 6 3 1
n=3: 1 7 29 41 29 7 1
n=4: 1 15 135 477 784 477 135 15 1
n=5: 1 31 642 5957 27375 41695 27375 5957 642 31 1
n=6: 1 63 3199 87477 1554077 7109189 21937982 7109189 1554077 87477 3199 63 1
n=7: 1 127 16879 1604768 189213842 3559635761 733133160992 86322358307 733133160992 3559635761 189213842 1604768 16879 127 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. A256156, A256157, A256159, A058669