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 A177476 #16 Oct 02 2024 08:34:19
%S A177476 1,1,2,6,20,83,402,2245,14192,100650,792508,6859260,64772648,
%T A177476 662630653,7301841444,86212535179,1085834949064,14530898302390,
%U A177476 205897508769218,3079580500287978,48485072137150344,801518797091165406,13881049047327393608,251325130816997882224,4748240560493406374592
%N A177476 Number of partitions of order n avoiding the consecutive pattern 231'1.
%C A177476 To avoid 231'1 means not to have four consecutive letters such that if the third letter is removed, then in the obtained 3 letter word the smallest letter is the last one, and the largest letter is the second one.
%H A177476 S. Kitaev, <a href="https://doi.org/10.1016/j.dam.2006.09.011">Introduction to partially ordered patterns</a>, Discrete Applied Mathematics 155 (2007), 929-944.
%t A177476 ok[{x_, y_, _, z_}] := Not[x>z && y>z && y>x]; a[n_] := Length@ Select[ Permutations@ Range@ n, AllTrue[ Partition[#, 4, 1], ok] &]; a /@ Range[0, 9]
%Y A177476 Cf. A117156, A177470, A177471, A177472, A177473, A177475, A177477, A177478, A177479, A177480, A177481, A177482, A177483, A177484, A376694.
%K A177476 nonn
%O A177476 0,3
%A A177476 Signy Olafsdottir (signy06(AT)ru.is), May 09 2010
%E A177476 a(0), a(10)-a(14) from _Alois P. Heinz_, Mar 10 2020
%E A177476 a(15)-a(16) from _Giovanni Resta_, Mar 11 2020
%E A177476 a(17)-a(24) from _Max Alekseyev_, Oct 02 2024