This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A382233 #28 Apr 02 2025 23:20:18 %S A382233 1,3,6,18,45,135,378,1134,3324,9981,29733,89280,267273 %N A382233 Dimensions of the homogeneous component of degree n of the free unital Jordan algebra on 3 generators. %C A382233 First few terms coincide with A032120 but A032120(8) = 3321. This corresponds to the fact that A032120 gives dimensions of components of the free special Jordan algebra (which follows from Cohn 1959), and 3324 - 3321 = 3 is the dimension of the GL_3-orbit of the so called Glennie identity. %C A382233 The terms up to a(12) were computed using the Albert nonassociative algebra system. %D A382233 C. M. Glennie, Identities in Jordan algebras, pp. 307-313 of J. Leech, editor, Computational Problems in Abstract Algebra. Pergamon, Oxford, 1970. %D A382233 D. P. Jacobs, The Albert nonassociative algebra system: a progress report, pp. 41-44 of Proceedings of the International Symposium on Symbolic and Algebraic Computation, Association for Computing Machinery, New York, NY, USA, 1994. %H A382233 Albert nonassociative algebra system, <a href="https://people.computing.clemson.edu/~dpj/albertstuff/albert.html">Homepage</a> %H A382233 P. M. Cohn, <a href="https://doi.org/10.1112/plms/s3-9.4.503">Two embedding theorems for Jordan algebras</a>, Proceedings of the London Mathematical Society, Volume s3-9, Issue 4, October 1959, pp. 503-524. %e A382233 For n = 3, we have a(3)=18 since the following monomials form a basis: x(xx), x(xy), x(xz), x(yy), x(yz), x(zz), y(xx), y(xy), y(xz), y(yy), y(yz), y(zz), z(xx), z(xy), z(xz), z(yy), z(yz), z(zz), these are all commutative nonassociative monomials of degree 3, since the Jordan identity is of degree 4. %Y A382233 Cf. A001776, A032120. %K A382233 nonn,hard,more %O A382233 0,2 %A A382233 _Vladimir Dotsenko_, Mar 29 2025