A079243 -id:A079243

A079208

Number of isomorphism classes of associative non-commutative non-anti-associative anti-commutative closed binary operations on a set of order n, listed by class size.

+10
9

0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

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CROSSREFS

Row sums give A079243.

A079231

Number of isomorphism classes of non-associative non-commutative non-anti-associative non-anti-commutative closed binary operations on a set of order n.

+10
9

0, 0, 2187, 147067071

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COMMENTS

A079231(n)+A079233(n)+A079235(n)+A079237(n)+A079196(n)+A079241(n)+A079243(n)+A079245(n)+A063524(n)=A002489(n)

CROSSREFS

Cf. A079202, A079230, A079233, A079235, A079237, A079196, A079241, A079243, A079245, A063524.

A079233

Number of isomorphism classes of non-associative non-commutative non-anti-associative anti-commutative closed binary operations on a set of order n.

+10
9

0, 2, 992, 31853003

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COMMENTS

A079231(n)+A079233(n)+A079235(n)+A079237(n)+A079196(n)+A079241(n)+A079243(n)+A079245(n)+A063524(n)=A002489(n)

CROSSREFS

Cf. A079203, A079232, A079231, A079235, A079237, A079196, A079241, A079243, A079245, A063524.

A079235

Number of isomorphism classes of non-associative non-commutative anti-associative non-anti-commutative closed binary operations on a set of order n.

+10
9

0, 0, 8, 13138

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COMMENTS

A079231(n)+A079233(n)+A079235(n)+A079237(n)+A079196(n)+A079241(n)+A079243(n)+A079245(n)+A063524(n)=A002489(n)

CROSSREFS

Cf. A079204, A079234, A079231, A079233, A079237, A079196, A079241, A079243, A079245, A063524.

A079237

Number of isomorphism classes of non-associative non-commutative anti-associative anti-commutative closed binary operations on a set of order n.

+10
9

0, 2, 2, 4642

(list; graph; refs; listen; history; text; internal format)

COMMENTS

A079231(n)+A079233(n)+A079235(n)+A079237(n)+A079196(n)+A079241(n)+A079243(n)+A079245(n)+A063524(n)=A002489(n)

CROSSREFS

Cf. A079205, A079236, A079231, A079233, A079235, A079196, A079241, A079243, A079245, A063524.

A079245

Number of isomorphism classes of associative commutative non-anti-associative non-anti-commutative closed binary operations on a set of order n.

+10
9

0, 3, 12, 58

(list; graph; refs; listen; history; text; internal format)

COMMENTS

A079231(n)+A079233(n)+A079235(n)+A079237(n)+A079196(n)+A079241(n)+A079243(n)+A079245(n)+A063524(n)=A002489(n)

CROSSREFS

Cf. A079209, A079244, A079231, A079233, A079235, A079237, A079196, A079241, A079243, A063524.

A079241

Number of isomorphism classes of associative non-commutative non-anti-associative non-anti-commutative closed binary operations on a set of order n.

+10
8

0, 0, 0, 10, 127, 1588, 26487, 1610379, 3683808608

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FORMULA

A079231(n) + A079233(n) + A079235(n) + A079237(n) + A079196(n) + a(n) + A079243(n) + A079245(n) + A063524(n) = A002489(n).

a(n) = A027851(n) - A001426(n) - A079243(n). - Andrew Howroyd, Jan 27 2022

CROSSREFS

Cf. A079240 (labeled case), A079231, A079233, A079235, A079237, A079196, A079243, A079245, A063524.

A079242

Number of associative non-commutative non-anti-associative anti-commutative closed binary operations on a set of order n.

+10
8

0, 0, 2, 2, 8, 2, 122, 2, 1682

(list; graph; refs; listen; history; text; internal format)

CROSSREFS

Cf. A079208, A079243 (isomorphism classes), A079230, A079232, A079234, A079236, A079195, A079240, A079244, A063524.