A294763 - OEIS

%I #18 Mar 21 2021 21:21:04

%S 1,1,2,6,21,73,238,714,1962,4957,11604,25390,52361,102533,191868,

%T 344970,598682,1006793,1646094,2624054,4088421,6239089,9342610,

%U 13749770,19916690,28429957,40036336,55677662,76531561,104058701,140057328,186725898,246734674,323307217,420312762

%N Number of permutations of [n] avoiding {4231, 1324, 1234}.

%H Vincenzo Librandi, <a href="/A294763/b294763.txt">Table of n, a(n) for n = 0..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 [math.CO] (2017), Table 2 No 73.

%F a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n > 10. - _Chai Wah Wu_, Oct 22 2018

%p -(x^10-15*x^8+55*x^7-111*x^6+149*x^5-141*x^4+89*x^3-37*x^2+9*x-1)/(x-1)^10   ;

%p taylor(%,x=0,40) ;

%p gfun[seriestolist](%) ;

%t CoefficientList[Series[-(x^10 - 15 x^8 + 55 x^7 - 111 x^6 + 149 x^5 - 141 x^4 + 89 x^3 - 37 x^2 + 9 x - 1) / (x - 1)^10, {x, 0, 40}], x] (* _Vincenzo Librandi_, Oct 23 2018 *)

%K nonn,easy

%O 0,3

%A _R. J. Mathar_, Nov 08 2017