A202180 -id:A202180 - cp's OEIS frontend

A202178 Triangle read by rows: T(n,k) = number of n-element unlabeled connected N-free posets of height k (1 <= k <= n).

1, 0, 1, 0, 2, 1, 0, 3, 5, 1, 0, 4, 17, 9, 1, 0, 5, 45, 50, 14, 1, 0, 6, 115, 218, 114, 20, 1, 0, 7, 278, 851, 709, 224, 27, 1, 0, 8, 679, 3161, 3818, 1867, 398, 35, 1, 0, 9, 1666, 11507, 19042, 13113, 4276, 657, 44, 1, 0, 10, 4167, 41837, 91383, 83222, 37898, 8845, 1025, 54, 1

Offset: 1

N. J. A. Sloane, Dec 13 2011

			Triangle begins:
1
0 1
0 2 1
0 3 5 1
0 4 17 9 1
0 5 45 50 14 1
0 6 115 218 114 20 1
0 7 278 851 709 224 27 1
0 8 679 3161 3818 1867 398 35 1
0 9 1666 11507 19042 13113 4276 657 44 1
0 10 4167 41837 91383 83222 37898 8845 1025 54 1
...

Soheir M. Khamis, Height counting of unlabeled interval and N-free posets, Discrete Math. 275 (2004), no. 1-3, 165-175.

See A202179 for another version. Row sums give A202180.

A202179 Triangle read by rows: T(n,k) = number of n-element unlabeled connected N-free posets of height k (2 <= k <= n).

Original entry on oeis.org

1, 2, 1, 3, 5, 1, 4, 17, 9, 1, 5, 45, 50, 14, 1, 6, 115, 218, 114, 20, 1, 7, 278, 851, 709, 224, 27, 1, 8, 679, 3161, 3818, 1867, 398, 35, 1, 9, 1666, 11507, 19042, 13113, 4276, 657, 44, 1, 10, 4167, 41837, 91383, 83222, 37898, 8845, 1025, 54, 1

Offset: 2

N. J. A. Sloane, Dec 13 2011

			Triangle begins: 1
2 1
3 5 1
4 17 9 1
5 45 50 14 1
6 115 218 114 20 1
7 278 851 709 224 27 1
8 679 3161 3818 1867 398 35 1
9 1666 11507 19042 13113 4276 657 44 1
10 4167 41837 91383 83222 37898 8845 1025 54 1
...

Soheir M. Khamis, Height counting of unlabeled interval and N-free posets, Discrete Math. 275 (2004), no. 1-3, 165-175.

See A202178 for another version. Row sums give A202180.

A349367 Number of n-element unlabeled disconnected N-free posets.

Original entry on oeis.org

0, 1, 2, 6, 18, 65, 241, 984, 4250, 19590, 95484, 491459, 2660030, 15100494, 89648378

Offset: 1

Salah Uddin Mohammad, Nov 15 2021

Soheir M. Khamis, Height counting of unlabeled interval and N-free posets, Discrete Math. 275 (2004), no. 1-3, 165-175.
Salah Uddin Mohammad, Md. Shah Noor, and Md. Rashed Talukder, An Exact Enumeration of the Unlabeled Disconnected Posets, J. Int. Seq., Vol. 25 (2022), Article 22.5.4.

Cf. A202182, A202180.

a(n) = A202182(n) - A202180(n).

A350783 Triangle read by rows: T(n,k) is the number of n-element unlabeled N-free posets with k connected components.

Original entry on oeis.org

1, 1, 1, 3, 1, 1, 9, 4, 1, 1, 31, 12, 4, 1, 1, 115, 46, 13, 4, 1, 1, 474, 173, 49, 13, 4, 1, 1, 2097, 727, 188, 50, 13, 4, 1, 1, 9967, 3195, 795, 191, 50, 13, 4, 1, 1, 50315, 15017, 3502, 810, 192, 50, 13, 4, 1, 1

Offset: 1

Salah Uddin Mohammad, Jan 16 2022

			Triangle begins:
      1;
      1,     1;
      3,     1,    1;
      9,     4,    1,   1;
     31,    12,    4,   1,   1;
    115,    46,   13,   4,   1,  1;
    474,   173,   49,  13,   4,  1,  1;
   2097,   727,  188,  50,  13,  4,  1, 1;
   9967,  3195,  795, 191,  50, 13,  4, 1, 1;
  50315, 15017, 3502, 810, 192, 50, 13, 4, 1, 1;
  ...

Salah Uddin Mohammad, Md. Shah Noor, and Md. Rashed Talukder, An Exact Enumeration of the Unlabeled Disconnected Posets, J. Int. Seq., Vol. 25 (2022), Article 22.5.4.

Row sums give A202182.
Column 1 is A202180.
Cf. A263864 (all posets), A349488 (disconnected).

cp's OEIS Frontend

A202178 Triangle read by rows: T(n,k) = number of n-element unlabeled connected N-free posets of height k (1 <= k <= n).

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A202179 Triangle read by rows: T(n,k) = number of n-element unlabeled connected N-free posets of height k (2 <= k <= n).

Views

Author

Keywords

Examples

Links

Crossrefs

A349367 Number of n-element unlabeled disconnected N-free posets.

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Formula

A350783 Triangle read by rows: T(n,k) is the number of n-element unlabeled N-free posets with k connected components.

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Author

Keywords

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