A294708 - OEIS

%I #14 Mar 21 2021 21:39:05

%S 1,1,2,6,21,69,190,446,927,1745,3036,4960,7701,11467,16490,23026,

%T 31355,41781,54632,70260,89041,111375,137686,168422,204055,245081,

%U 292020,345416,405837,473875,550146,635290,729971,834877,950720,1078236,1218185,1371351,1538542,1720590

%N Number of permutations of [n] avoiding {4231, 2143, 1234}.

%H Colin Barker, <a href="/A294708/b294708.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 4.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F From _Colin Barker_, Nov 10 2017: (Start)

%F G.f.: (1 - 4*x + 7*x^2 - 4*x^3 + 6*x^4 + 8*x^5 + 4*x^6 + 4*x^7 + 6*x^8 - 6*x^9 + 2*x^10) / (1 - x)^5.

%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>10.

%F a(n) = (1/6)*(786 - 787*n + 333*n^2 - 68*n^3 + 6*n^4) for n>5.

%F (End)

%p cn := [1,-4,7,-4,6,8,4,4,6,-6,2] ;

%p p := add(cn[i]*x^(i-1),i=1..nops(cn)) ;

%p q := (1-x)^5 ;

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

%p gfun[seriestolist](%) ;

%o (PARI) Vec((1 - 4*x + 7*x^2 - 4*x^3 + 6*x^4 + 8*x^5 + 4*x^6 + 4*x^7 + 6*x^8 - 6*x^9 + 2*x^10) / (1 - x)^5 + O(x^40)) \\ _Colin Barker_, Nov 10 2017

%K nonn,easy

%O 0,3

%A _R. J. Mathar_, Nov 07 2017