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A202534
Number of symmetric, reflexive, non-transitive relations on n elements.
0
0, 0, 3, 49, 972, 32565, 2096275, 268431316, 68719455589, 35184371972857, 36028797018285398, 73786976294833992867, 302231454903657266032107, 2475880078570760549607349126, 40564819207303340847893119613487, 1329227995784915872903807049800202429
OFFSET
1,3
COMMENTS
Of the values shown, only 3 is prime. Are there any other prime values in the sequence? - Jonathan Vos Post, Dec 29 2011
FORMULA
a(n) = 2^(n*(n-1)/2) - A000110(n) = A006125(n) - A000110(n).
EXAMPLE
The first symmetric, reflexive, nontransitive relation occurs for n=3: omitting a non-identical couple (a,b) from the total relation gives such a relation (and for n=3, this is the only way). There are 3 ways to choose this couple.
PROG
(Sage) def a(n): return 2^(n*(n-1)/2) - bell_number(n)
CROSSREFS
Sequence in context: A203760 A208935 A355882 * A277497 A173174 A302466
KEYWORD
nonn
AUTHOR
Bert Seghers, Dec 20 2011
STATUS
approved