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%I #17 Sep 04 2022 21:00:02
%S 1,2,6,21,71,204,479,951,1687,2764,4269,6299,8961,12372,16659,21959,
%T 28419,36196,45457,56379,69149,83964,101031,120567,142799,167964,
%U 196309,228091,263577,303044,346779,395079,448251,506612,570489,640219,716149,798636
%N Number of permutations of length n which avoid the patterns 1243, 2341, 4321.
%H Colin Barker, <a href="/A116825/b116825.txt">Table of n, a(n) for n = 1..1000</a>
%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 20.
%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.: x*(1 - 3*x + 6*x^2 + x^3 + 11*x^4 + 8*x^5 - 13*x^6 - 15*x^7 + 16*x^8 - 2*x^9) / (1 - x)^5.
%F For n >= 6, a(n) = (5*n^4 - 16*n^3 + 43*n^2 - 752*n + 2388)/12. - _Franklin T. Adams-Watters_, Sep 16 2006
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - _Wesley Ivan Hurt_, Sep 04 2022
%t CoefficientList[Series[(1 - 3*x + 6*x^2 + x^3 + 11*x^4 + 8*x^5 - 13*x^6 - 15*x^7 + 16*x^8 - 2*x^9)/(1 - x)^5, {x, 0, 40}], x] (* _Wesley Ivan Hurt_, Sep 04 2022 *)
%o (PARI) Vec(x*(1 - 3*x + 6*x^2 + x^3 + 11*x^4 + 8*x^5 - 13*x^6 - 15*x^7 + 16*x^8 - 2*x^9) / (1 - x)^5 + O(x^50)) \\ _Colin Barker_, Oct 24 2017
%K nonn,easy
%O 1,2
%A _Lara Pudwell_, Feb 26 2006
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