A256157 -id:A256157 - cp's OEIS frontend

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

Max Alekseyev, Mar 16 2015

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

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

			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

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

Cf. A256157, A256158, A256159, A053534

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

Original entry on oeis.org

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

Max Alekseyev, Mar 16 2015

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

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

			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

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

Cf. A256156, A256157, A256159, A058669

A256159 Number of 2-polymatroids on n labeled points.

Original entry on oeis.org

1, 3, 14, 115, 2040, 109707, 39445994, 1560089623047

Offset: 0

Max Alekseyev, Mar 16 2015

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

Row sums of A256158.

Cf. A256156, A256157, A058673.

cp's OEIS Frontend

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

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

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A256159 Number of 2-polymatroids on n labeled points.

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