A294766 - OEIS

%I #11 Mar 21 2021 21:16:17

%S 1,1,2,6,21,74,248,784,2355,6785,18897,51177,135358,350788,893038,

%T 2237998,5530485,13496371,32566359,77785039,184083080,432004206,

%U 1006097772,2326777196,5346673751,12213795349,27749494413,62729986469,141146690370,316216935240,705582559642

%N Number of permutations of [n] avoiding {4312, 1432, 1234}.

%H Colin Barker, <a href="/A294766/b294766.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 119

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (13,-74,242,-501,681,-608,344,-112,16).

%F G.f.: (1 - 12*x + 63*x^2 - 188*x^3 + 350*x^4 - 419*x^5 + 317*x^6 - 138*x^7 + 26*x^8 - x^9) / ((1 - x)^5*(1 - 2*x)^4).

%F From _Colin Barker_, Nov 09 2017: (Start)

%F a(n) = (1/96)*(-6*(-16+2^n) + (-136+123*2^n)*n - 4*(11+3*2^(1+n))*n^2 + (-8+3*2^n)*n^3 - 4*n^4).

%F a(n) = 13*a(n-1) - 74*a(n-2) + 242*a(n-3) - 501*a(n-4) + 681*a(n-5) - 608*a(n-6) + 344*a(n-7) - 112*a(n-8) + 16*a(n-9) for n>9.

%F (End)

%p (-350*x^4-63*x^2+419*x^5-26*x^8+138*x^7-317*x^6+188*x^3+x^9-1+12*x)/((2*x-1)^4*(x-1)^5)   ;

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

%p gfun[seriestolist](%) ;

%o (PARI) Vec((1 - 12*x + 63*x^2 - 188*x^3 + 350*x^4 - 419*x^5 + 317*x^6 - 138*x^7 + 26*x^8 - x^9) / ((1 - x)^5*(1 - 2*x)^4) + O(x^30)) \\ _Colin Barker_, Nov 09 2017

%K nonn,easy

%O 0,3

%A _R. J. Mathar_, Nov 08 2017