A350772 Triangle read by rows: T(n,k) is the number of n-element unlabeled series-parallel posets with k connected components.

1, 1, 1, 3, 1, 1, 9, 4, 1, 1, 30, 12, 4, 1, 1, 103, 45, 13, 4, 1, 1, 375, 160, 48, 13, 4, 1, 1, 1400, 613, 175, 49, 13, 4, 1, 1, 5380, 2354, 680, 178, 49, 13, 4, 1, 1

Offset

1,4

Links

Table of n, a(n) for n=1..45.

S. U. Mohammad, M. R. Talukder, and S. N. Begum, Enumeration of unlabeled series-parallel posets by using the poset matrix, Palestine Journal of Mathematics, 14(1) (2025), 217-232.

Example

Triangle begins:
     1;
     1,    1;
     3,    1,   1;
     9,    4,   1,   1;
    30,   12,   4,   1,  1;
   103,   45,  13,   4,  1,  1;
   375,  160,  48,  13,  4,  1, 1;
  1400,  613, 175,  49, 13,  4, 1, 1;
  5380, 2354, 680, 178, 49, 13, 4, 1, 1;
  ...

Crossrefs

Row sums give A003430.

Column 1 is A007453.

Cf. A263864 (all posets), A349488 (disconnected).

Sequence in context: A069605 A080510 A378163 * A350783 A124496 A074881

Adjacent sequences: A350769 A350770 A350771 * A350773 A350774 A350775

Keyword

nonn,tabl,more

Author

Salah Uddin Mohammad, Jan 14 2022

Status

approved