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Number of permutations of length n which avoid the patterns 2134, 3421, 4312.
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%I #19 Nov 08 2017 04:21:49

%S 1,2,6,21,71,200,465,929,1667,2766,4325,6455,9279,12932,17561,23325,

%T 30395,38954,49197,61331,75575,92160,111329,133337,158451,186950,

%U 219125,255279,295727,340796

%N Number of permutations of length n which avoid the patterns 2134, 3421, 4312.

%H D. Callan, T. Mansour, <a href="http://arxiv.org/abs/1705.00933">Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns</a>, arXiv:1705.00933 (2017), Table 2 No 19.

%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 (5,-10,10,-5,1).

%F G.f.: -((6x^8-7x^7-7x^6+4x^5+11x^4+x^3+6x^2-3x+1)*x)/(x-1)^5.

%F For n >= 5, a(n) = (n^4 - 5n^3 + 9n^2 - 57n + 202)/2. - _Franklin T. Adams-Watters_, Sep 16 2006

%t (1 - 3x + 6x^2 + x^3 + 11x^4 + 4x^5 - 7x^6 - 7x^7 + 6x^8)/(1 - x)^5 + O[x]^30 // CoefficientList[#, x]& (* _Jean-François Alcover_, May 06 2017 *)

%K nonn,easy

%O 1,2

%A _Lara Pudwell_, Feb 26 2006