%I #14 Oct 12 2020 12:31:39

%S 1,2,5,12,22,32,42,52,62,72,82,92,102,112,122,132,142,152,162,172,182,

%T 192,202,212,222,232,242,252,262,272,282,292,302,312,322,332,342,352,

%U 362,372,382,392,402,412,422,432,442,452,462,472,482,492,502,512,522

%N Number of permutations of length n which avoid the patterns 321, 2134, 3412.

%H Colin Barker, <a href="/A116727/b116727.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_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F G.f.: x*(1 + 2*x^2 + 4*x^3 + 3*x^4) / (1 - x)^2.

%F For n >= 4, a(n) = 10*n - 28. - _Franklin T. Adams-Watters_, Sep 16 2006

%F a(n) = 2*a(n-1) - a(n-2) for n=5. - _Colin Barker_, Oct 24 2017

%t Join[{1, 2, 5}, LinearRecurrence[{2, -1}, {12, 22}, 100]] (* _Jean-François Alcover_, Oct 12 2020 *)

%o (PARI) Vec(x*(1 + 2*x^2 + 4*x^3 + 3*x^4) / (1 - x)^2 + O(x^70)) \\ _Colin Barker_, Oct 24 2017

%K nonn,easy

%O 1,2

%A _Lara Pudwell_, Feb 26 2006