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 A217711 #16 Nov 27 2018 04:45:35
%S A217711 1,16,144,1016,6271,35584,190628,979496,4876530,23686560,112796176,
%T A217711 528495600,2442949979,11163970432,50520351612,226688100104,
%U A217711 1009648508590,4467591809376,19654294688768,86018255452048,374715017442966,1625489878136576,7024392489806344
%N A217711 Total number of 321 patterns in the set of permutations avoiding 123.
%C A217711 a(n) is the total number of occurrences of 321 patterns in the set of all 123-avoiding n-permutations.
%H A217711 Cheyne Homberger, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v19i3p43">Expected patterns in permutation classes</a>, Electronic Journal of Combinatorics, 19(3) (2012), P43.
%F A217711 G.f.: 1/2*(32*x^4 - 88*x^3 + 52*x^2 + sqrt(-4*x + 1)*(36*x^3 - 34*x^2 + 10*x - 1) - 12*x + 1)/(64*x^4 - 48*x^3 + 12*x^2 - x).
%F A217711 Conjecture: -(n+1)*(25*n-3314)*a(n) -5*n*(5*n+9446)*a(n-1) +2*(594*n^2 +128863*n -142613)*a(n-2) +16*(-119*n^2-39230*n+87888)*a(n-3) -32*(2*n-7)*(53*n-8687)*a(n-4)=0. - _R. J. Mathar_, Oct 08 2016
%e A217711 a(3) = 1 since there is only one 321 pattern in the set {132, 213, 231, 312, 321}.
%K A217711 nonn
%O A217711 3,2
%A A217711 _Cheyne Homberger_, Mar 20 2013