%I #14 Jan 21 2016 16:42:51
%S 1,2,5,12,25,50,97,184,345,642,1189,2196,4049,7458,13729,25264,46481,
%T 85506,157285,289308,532137,978770,1800257,3311208,6090281,11201794,
%U 20603333,37895460,69700641,128199490,235795649,433695840,797691041
%N Number of permutations of length n which avoid the patterns 231, 1432, 4123.
%H Harvey P. Dale, <a href="/A116734/b116734.txt">Table of n, a(n) for n = 1..1000</a>
%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 (3, -2, 0, -1, 1).
%F G.f.: A(x) = -{x(x^2+x^3+1-x)}/{(x-1)^2(x^3+x^2+x-1)}
%F a(n)=A000213(n+2)-n-1. [From _R. J. Mathar_, Aug 05 2008]
%F a(0)=0, a(1)=1, a(2)=2, then a(n) = a(n-1) + a(n-2) + a(n-3) + 2*n - 4. [From _Gerald McGarvey_, Oct 06 2009]
%t LinearRecurrence[{3,-2,0,-1,1},{1,2,5,12,25},40] (* _Harvey P. Dale_, Jan 21 2016 *)
%K nonn,easy
%O 1,2
%A _Lara Pudwell_, Feb 26 2006
%E Extended beyond a(30) by _R. J. Mathar_, Aug 05 2008