A202534 Number of symmetric, reflexive, non-transitive relations on n elements.

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

Links

Table of n, a(n) for n=1..16.

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

Adjacent sequences: A202531 A202532 A202533 * A202535 A202536 A202537

Keyword

nonn

Author

Bert Seghers, Dec 20 2011

Status

approved