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 A260579 #19 Mar 18 2018 17:37:52 %S A260579 1,2,106,5976,387564,27247446,2020632046,155622020610,12327937844924, %T A260579 998103225615208 %N A260579 Labelings of n diamond-shaped posets with 4 vertices per diamond where the labels follow the poset relations whose associated reading permutation avoids 321 in the classical sense. %C A260579 By diamond-shaped poset with 4 vertices, we mean a poset on four elements with e_1 < e_2, e_1 < e_3, e_2 < e_4, e_3 < e_4, and no order relations between e_2 and e_3. In the Hasse diagram for such a poset, we have a least element, two elements in the level above, and one element in the top level, so the diagram resembles a diamond. The associated permutation is the permutation obtained by reading the labels of each poset by levels left to right, starting with the least element. %C A260579 Additional terms were provided by David Bevan. %H A260579 M. Paukner, L. Pepin, M. Riehl, and J. Wieser, <a href="http://arxiv.org/abs/1511.00080">Pattern Avoidance in Task-Precedence Posets</a>, arXiv:1511.00080 [math.CO], 2015. %H A260579 Manda Riehl, <a href="/A260579/a260579.png">A 321-avoiding diamond with associated permutation 1234.</a> %e A260579 For a single diamond (n=1) poset with 4 vertices, we must label the least element 1 and the greatest element 4, and the two central elements can be labeled either 2, 3 or 3, 2 respectively. Thus the associated permutations are 1234 and 1324. %Y A260579 Cf. A260331, A260332. %K A260579 nonn,more %O A260579 0,2 %A A260579 _Manda Riehl_, Jul 29 2015