A079207 - OEIS

%I #11 Jan 27 2022 15:41:52

%S 0,0,0,0,0,0,4,6,0,0,0,4,4,0,46,73,0,0,0,0,4,0,0,8,0,2,36,0,43,2,473,

%T 1020,0,0,0,0,0,4,0,0,0,0,8,0,0,4,0,36,0,0,0,0,84,0,0,38,415,0,758,32,

%U 6682,18426,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,8

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

%C Elements per row: 1,1,2,4,8,16,30,... (given by A027423, number of positive divisors of n!)

%H Andrew Howroyd, <a href="/A079207/b079207.txt">Table of n, a(n) for n = 0..217</a> (rows 0..8)

%H C. van den Bosch, <a href="https://web.archive.org/web/20071014230143/http://cosmos.ucc.ie/~cjvdb1/html/binops.shtml">Closed binary operations on small sets</a>

%H <a href="/index/Se#semigroups">Index entries for sequences related to semigroups</a>

%F A079202(n,k) + A079203(n,k) + A079204(n,k) + A079205(n,k) + A079197(n,k) + A079208(n,k) + T(n,k) + A079201(n,k) = A079171(n,k).

%F A079240(n) = Sum_{k>=1} T(n,k)*A079210(n,k).

%F T(n,k) = A079175(n,k) - A079201(n,k) - A079208(n,k). - _Andrew Howroyd_, Jan 27 2022

%e Triangle T(n,k) begins:

%e   0;

%e   0;

%e   0, 0;

%e   0, 0, 4, 6;

%e   0, 0, 0, 4, 4, 0, 46, 73;

%e   0, 0, 0, 0, 4, 0, 0, 8, 0, 2, 36, 0, 43, 2, 473, 1020;

%e   ...

%Y Row sums give A079241.

%Y Cf. A027423 (row lengths), A079175, A079201, A079202, A079203, A079204, A079205, A079197, A079208, A079209, A079240.

%K nonn,tabf

%O 0,7

%A Christian van den Bosch (cjb(AT)cjb.ie), Jan 03 2003

%E a(0)=0 prepended and terms a(16) and beyond from _Andrew Howroyd_, Jan 27 2022