Question about A001330 and A001331
Christian G. Bower
bowerc at usa.net
Thu Jan 15 19:12:08 CET 2004
In the sequence A001330:
ID Number: A001330 (Formerly M5398 and N2346)
URL: http://www.research.att.com/projects/OEIS?Anum=A001330
Sequence: 1,136,64573605
Name: n-element algebras with 2 binary operations.
References M. A. Harrison, The number of isomorphism types of finite
algebras,
Proc. Amer. Math. Soc., 17 (1966), 731-737.
I take the description as the isomorphisms classes of a set A with two
functions f1,f2 : AxA -> A
I calculate:
1 136 64573605 768614338015543296 ...
so all is well.
However in the sequence A001331:
ID Number: A001331 (Formerly M5395 and N2344)
URL: http://www.research.att.com/projects/OEIS?Anum=A001331
Sequence: 1,130,1270932917454
Name: n-element algebras with 1 ternary operation.
References M. A. Harrison, The number of isomorphism types of finite
algebras,
Proc. Amer. Math. Soc., 17 (1966), 731-737.
I take the description as the isomorphisms classes of a set A with one
function f : AxAxA -> A
I calculate
1 136 1270933717887 14178431955039102651224805804387336192 ...
and all is not well.
a(2) certainly cannot be 130. Since there are 256 tables, 130 classes
implies only 4 classes symmetric under (12). Well here are 6 obvious ones:
f(a,b,c) = a
f(a,b,c) = !a
f(a,b,c) = b
f(a,b,c) = !b
f(a,b,c) = c
f(a,b,c) = !c
and I thought of some more not so obvious ones.
So is the sequence in error, or is it counting something else.
I don't have access to the source so I can't tell.
I would like to submit the sequence I just described. The question is
whether to submit it as a new sequence or to replace the terms of
A001331.
Christian
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