A361954 Triangle read by rows: T(n,k) is the number of unlabeled connected weakly graded (ranked) posets with n elements and rank k.

1, 0, 1, 0, 2, 1, 0, 4, 5, 1, 0, 10, 23, 8, 1, 0, 27, 107, 56, 11, 1, 0, 88, 557, 388, 98, 14, 1, 0, 328, 3271, 2888, 839, 149, 17, 1, 0, 1460, 22424, 23900, 7512, 1470, 209, 20, 1, 0, 7799, 183273, 226807, 73405, 14715, 2308, 278, 23, 1

Offset: 1

Author

Andrew Howroyd, Mar 31 2023

Keywords

• nonn
• tabl

Comments

Here weakly graded means that there exists a rank function rk from the poset to the integers such that whenever v covers w in the poset, we have rk(v) = rk(w) + 1.

Examples

			Triangle begins:
  1;
  0,   1;
  0,   2,    1;
  0,   4,    5,    1;
  0,  10,   23,    8,   1;
  0,  27,  107,   56,  11,   1;
  0,  88,  557,  388,  98,  14,  1;
  0, 328, 3271, 2888, 839, 149, 17, 1;
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..820 (rows 1..40)
• Wikipedia, Graded poset.

Crossrefs

Column k=2 is A007776.

Row sums are A361955.

Cf. A342500, A361953 (not necessarily connected).

Programs

PARI

\\ See PARI link in A361953 for program code.
{ my(A=A361954tabl(8)); for(i=1, #A, print(A[i, 1..i])) }