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
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
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