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 A118641 #16 Nov 28 2023 08:58:38 %S A118641 1,33,2333 %N A118641 Number of nonisomorphic finite non-associative, invertible loops of order n. %C A118641 These are non-associative loops in which every element has a unique inverse and it includes IP, Moufang and Bol loops [Cawagas]. The data were generated and checked by a supercomputer of 48 Pentium II 400 processors, specially built for automated reasoning, in about three days. In general, a loop is a quasigroup with an identity element e such that xe = x and ex = x for any x in the quasigroup. All groups are loops. A quasigroup is a groupoid G such that for all a and b in G, there exist unique c and d in G such that ac = b and da = b. Hence a quasigroup is not required to have an identity element, nor be associative. Equivalently, one can state that quasigroups are precisely groupoids whose multiplication tables are Latin squares (possibly empty). %D A118641 Cawagas, R. E., Terminal Report: Development of the Theory of Finite Pseudogroups (1998). Research supported by the National Research Council of the Philippines (1996-1998) under Project B-88 and B-95. %H A118641 Hantao Zhang, <a href="http://aarinc.org/Newsletters/046-2000-01.html#nafil">Generation of NAFILs of Order 7</a>, Association for Automated Reasoning, No. 46, 2000. %H A118641 John Pedersen, <a href="http://www.math.usf.edu/~eclark/algctlg/loops.html">Loops.</a> %e A118641 a(5) = 1 (which is non-Abelian). %e A118641 a(6) = 33 (7 Abelian + 26 non-Abelian). %e A118641 a(7) = 2333 (16 Abelian + 2317 non-Abelian). %Y A118641 Cf. A001329. %K A118641 nonn,bref,more %O A118641 5,2 %A A118641 _Jonathan Vos Post_, May 10 2006