%I #16 Oct 20 2017 14:37:04

%S 1,2,5,12,26,58,131,295,662,1487,3342,7510,16874,37915,85195,191432,

%T 430143,966522,2171756,4879892,10965017,24638169,55361464,124396081,

%U 279515456,628065528,1411250432,3171050937,7125286777,16010374058,35974983957,80835055196

%N Number of permutations of length n which avoid the patterns 321, 2341, 4123.

%H Colin Barker, <a href="/A116716/b116716.txt">Table of n, a(n) for n = 1..1000</a>

%H David Lonoff and Jonah Ostroff, <a href="https://www.math.upenn.edu/~lonoff/pdfs/spatp.pdf">Symmetric Permutations Avoiding Two Patterns</a>, Annals of Combinatorics 14 (1) pp.143-158 Springer, 2010; . - _N. J. A. Sloane_, Dec 27 2012

%H Lara Pudwell, <a href="http://faculty.valpo.edu/lpudwell/maple/webbook/bookmain.html">Systematic Studies in Pattern Avoidance</a>, 2005.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,1,1,-1).

%F G.f.: x*(1 + x)*(1 - x + 2*x^2 - x^3) / ((1 + x^2)*(1 - 2*x - x^2 + x^3)).

%F a(n) = 2*a(n-1) + a(n-3) + a(n-4) - a(n-5) for n>5. - _Colin Barker_, Oct 20 2017

%o (PARI) Vec(x*(1 + x)*(1 - x + 2*x^2 - x^3) / ((1 + x^2)*(1 - 2*x - x^2 + x^3)) + O(x^40)) \\ _Colin Barker_, Oct 20 2017

%K nonn,easy

%O 1,2

%A _Lara Pudwell_, Feb 26 2006