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A079243
Number of isomorphism classes of associative non-commutative non-anti-associative anti-commutative closed binary operations on a set of order n.
8
0, 0, 2, 2, 3, 2, 4, 2, 4
OFFSET
0,3
COMMENTS
The only closed binary operations that are both commutative and anti-commutative are those on sets of size <= 1. The significance of non-commutative (and non-anti-associative) in the name is that it excludes this possibility. Otherwise, the first two terms would be 1. - Andrew Howroyd, Jan 26 2022
FORMULA
A079231(n) + A079233(n) + A079235(n) + A079237(n) + A079196(n) + A079241(n) + a(n) + A079245(n) + A063524(n) = A002489(n).
Conjecture: a(n) = A000005(n) for n > 1. - Andrew Howroyd, Jan 26 2022
EXAMPLE
From Andrew Howroyd, Jan 26 2022: (Start)
The a(6) = 4 operations are the two shown below and their converses.
| 1 2 3 4 5 6 | 1 2 3 4 5 6
--+------------ --+------------
1 | 1 2 3 4 5 6 1 | 1 2 3 1 2 3
2 | 1 2 3 4 5 6 2 | 1 2 3 1 2 3
3 | 1 2 3 4 5 6 3 | 1 2 3 1 2 3
4 | 1 2 3 4 5 6 4 | 4 5 6 4 5 6
5 | 1 2 3 4 5 6 5 | 4 5 6 4 5 6
6 | 1 2 3 4 5 6 6 | 4 5 6 4 5 6
(End)
CROSSREFS
Row sums of A079208.
Sequence in context: A043261 A157986 A025479 * A093640 A320538 A343650
KEYWORD
nonn,more
AUTHOR
Christian van den Bosch (cjb(AT)cjb.ie), Jan 03 2003
EXTENSIONS
a(0)=0 prepended and a(5)-a(8) from Andrew Howroyd, Jan 26 2022
STATUS
approved