A049463 Number of basic interval orders of length n.

1, 2, 7, 34, 219, 1787, 17936, 216169, 3069552, 50562672, 953877927, 20389082457, 489301660818, 13080166471127, 386841424466953, 12581201258360820, 447574544428423114, 17333939484785264282, 727718718839603466267

Offset

2,2

Comments

One may represent a basic length n interval order using n distinct endpoints. The removal of any element from such an order yields an interval order with shorter length.

See the Wikipedia article for the definition of interval order.

References

Amy N. Myers, Basic Interval Orders, Order, Volume: 16, Issue: 3, 1999, pp. 261-275.

Links

Table of n, a(n) for n=2..20.

Sean A. Irvine, Java program (github)

Amy N. Myers, Home page at Bryn Mawr College.

Amy N. Myers, Basic Interval Orders, Order, Volume: 16, Issue: 3, 1999, pp. 261-275. [Paywall]

Amy N. Myers, Results in Enumeration and Topology of Interval Orders, Ph.D. Thesis at Dartmouth College.

David Radcliffe, Python script for sequence A049463

Wikipedia, Interval order

Formula

A recurrence in three variables exists.

Example

a(2)=1 since {[ 1,1 ],[ 2,2 ]} is the unique basic interval order with two distinct endpoints.

Crossrefs

Sequence in context: A185324 A135882 A143740 * A294466 A029894 A110313

Adjacent sequences: A049460 A049461 A049462 * A049464 A049465 A049466

Keyword

nonn,nice,easy

Author

Amy N. Myers (Amy.Myers(AT)Alum.Dartmouth.ORG)

Extensions

Edited by David Radcliffe, Aug 01 2021

Status

approved