A049463 - OEIS

%I #21 Aug 03 2021 18:27:09

%S 1,2,7,34,219,1787,17936,216169,3069552,50562672,953877927,

%T 20389082457,489301660818,13080166471127,386841424466953,

%U 12581201258360820,447574544428423114,17333939484785264282,727718718839603466267

%N Number of basic interval orders of length n.

%C 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.

%C See the Wikipedia article for the definition of interval order.

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

%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a049/A049463.java">Java program</a> (github)

%H Amy N. Myers, <a href="https://www.brynmawr.edu/people/amy-n-myers">Home page</a> at Bryn Mawr College.

%H Amy N. Myers, <a href="https://doi.org/10.1023/A:1006477416166">Basic Interval Orders</a>, Order, Volume: 16, Issue: 3, 1999, pp. 261-275. [Paywall]

%H Amy N. Myers, <a href="https://collections.dartmouth.edu/archive/object/dcdis/dcdis-myers1999">Results in Enumeration and Topology of Interval Orders</a>, Ph.D. Thesis at Dartmouth College.

%H David Radcliffe, <a href="https://gist.github.com/Radcliffe/a56187c144317e1f9ae31ebbf975fb90">Python script for sequence A049463</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Interval_order">Interval order</a>

%F A recurrence in three variables exists.

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

%K nonn,nice,easy

%O 2,2

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

%E Edited by _David Radcliffe_, Aug 01 2021