A361952 - OEIS

A361952

Array read by antidiagonals: T(n,k) is the number of unlabeled posets with n elements together with a function rk mapping each element to a rank between 1 and k such that whenever v covers w in the poset then rk(v) = rk(w) + 1.

1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 3, 4, 1, 0, 1, 4, 8, 8, 1, 0, 1, 5, 13, 21, 17, 1, 0, 1, 6, 19, 40, 58, 38, 1, 0, 1, 7, 26, 66, 126, 172, 94, 1, 0, 1, 8, 34, 100, 228, 420, 569, 258, 1, 0, 1, 9, 43, 143, 373, 816, 1537, 2148, 815, 1, 0, 1, 10, 53, 196, 571, 1412, 3140, 6342, 9538, 3038, 1, 0

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,8

COMMENTS

A poset is counted once for each admissible ranking function. This is an intermediate step in the computation of A361953 where each graded poset is counted exactly once.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..860 (first 41 antidiagonals).

EXAMPLE

Array begins:

============================================

n/k| 0 1 2 3 4 5 6 7 ...

---+----------------------------------------

0 | 1 1 1 1 1 1 1 1 ...

1 | 0 1 2 3 4 5 6 7 ...

2 | 0 1 4 8 13 19 26 34 ...

3 | 0 1 8 21 40 66 100 143 ...

4 | 0 1 17 58 126 228 373 571 ...