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

1,5

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.

Links

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

Wikipedia, Graded poset.

Example

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;
  ...

Prog

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

Crossrefs

Column k=2 is A007776.

Row sums are A361955.

Cf. A342500, A361953 (not necessarily connected).

Sequence in context: A073592 A164994 A269952 * A342500 A247268 A266867

Adjacent sequences: A361951 A361952 A361953 * A361955 A361956 A361957

Keyword

nonn,tabl

Author

Andrew Howroyd, Mar 31 2023

Status

approved