A361920 Number of unlabeled ranked posets with n elements.

1, 1, 2, 5, 16, 61, 280, 1501, 9394, 68647, 591570, 6108298, 77162708, 1219779207, 24648006828, 647865966973, 22437052221282, 1032905858402302, 63591727342096158, 5258562027225785955, 586001891321599337103, 88241281449605821921186, 17996565026907866304071630

Offset

0,3

Comments

A partially ordered set is ranked if there is a function from the poset elements to the integers such that the function value of a covering element is precisely one larger than the function value of the covered element. This is called graded by some authors.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..40

Example

For n=5, A000112(n) - a(n) = 63 - 61 = 2 because we have 2 posets with 5 elements that are not ranked: a<b<c<d  a<e<d  and  a<c<e  a<d  b<d  b<e where < means "is covered by". - Geoffrey Critzer, Oct 29 2023

Prog

(Sage) sum(1 for P in posets(n) if P.is_ranked())
(PARI) \\ See PARI link in A361953 for program code.
A361920seq(20) \\ Andrew Howroyd, Apr 01 2023

Crossrefs

Row sums of A361953.

Cf. A000112, A001833 (labeled), A223911, A361912, A361955.

Sequence in context: A000111 A007976 A058259 * A368318 A369400 A033543

Adjacent sequences: A361917 A361918 A361919 * A361921 A361922 A361923

Keyword

nonn

Author

Martin Rubey, Mar 29 2023

Extensions

Terms a(8) and beyond from Andrew Howroyd, Mar 31 2023

Status

approved