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Number of permutations of length n which avoid the patterns 312, 2341, 4321.
2

%I #9 Oct 20 2017 14:36:54

%S 1,2,5,12,25,54,120,265,580,1272,2796,6143,13488,29619,65053,142873,

%T 313771,689095,1513390,3323699,7299465,16031000,35207128,77321545,

%U 169812767,372941033,819049274,1798787604,3950478790,8676000808,19054143661,41846514135

%N Number of permutations of length n which avoid the patterns 312, 2341, 4321.

%H Colin Barker, <a href="/A116715/b116715.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 (1,1,2,3,1).

%F G.f.: x*(1 + x)*(1 + 2*x^2 + x^3) / (1 - x - x^2 - 2*x^3 - 3*x^4 - x^5).

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

%o (PARI) Vec(x*(1 + x)*(1 + 2*x^2 + x^3) / (1 - x - x^2 - 2*x^3 - 3*x^4 - x^5) + O(x^40)) \\ _Colin Barker_, Oct 20 2017

%K nonn,easy

%O 1,2

%A _Lara Pudwell_, Feb 26 2006