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A049463
Number of basic interval orders of length n.
1
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
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.
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: A135882 A376527 A143740 * A294466 A029894 A110313
KEYWORD
nonn,nice,easy
AUTHOR
Amy N. Myers (Amy.Myers(AT)Alum.Dartmouth.ORG)
EXTENSIONS
Edited by David Radcliffe, Aug 01 2021
STATUS
approved