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 A139561 #5 Jan 31 2018 18:22:57 %S A139561 1,3,9,27,78,216,568,1416,3327 %N A139561 Growth function for the relatively free monoid on three generators with identity xyzyx = yxzxy. %C A139561 A semigroup which satisfies the identity xyzyx=yxzxy is called nilpotent of class 2 in the Malcev sense. Initially this sequence looks very like A140348, which counts the words that are distinct in the free nil-2 group. %C A139561 The sequences first differ at n=7, where there are six equations that hold for the group but do not follow from the Malcev identity, e.g. abccaab = caabbca. Cancellation is not assumed and does not hold, so despite the fact that the former equation does not follow from the Malcev identity, aabccaab = acaabbca does follow. %C A139561 Shneerson has shown that this sequence grows roughly like some power of n^logn . Contrast to A140348, which has polynomial growth. %D A139561 L. M. Shneerson, Relatively free semigroups of intermediate growth, J. Algebra, 235 (2001) 484-546. %e A139561 Substituting x->a, y->b, z->1 in the identity gives abba=baab, this is the smallest example. %e A139561 Substituting x->ab, y->b, z->c in the identity gives abbcbab=babcabb. %Y A139561 Cf. A140348. %K A139561 nonn %O A139561 0,2 %A A139561 _David S. Newman_ and _Moshe Shmuel Newman_, Jun 10 2008