A294762 - OEIS

%I #11 Nov 11 2017 11:31:30

%S 1,1,2,6,21,73,237,702,1881,4577,10216,21158,41097,75561,132523,

%T 223134,362589,571137,875246,1308934,1915277,2748105,3873897,5373886,

%U 7346385,9909345,13203156,17393702,22675681,29276201,37458663,47526942,59829877,74766081,92789082

%N Number of permutations of [n] avoiding {4231, 1243, 1234}.

%H Colin Barker, <a href="/A294762/b294762.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 71.

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).

%F G.f.: (1 - 7*x + 22*x^2 - 38*x^3 + 43*x^4 - 25*x^5 + 17*x^6 + 2*x^7 - 4*x^8) / (1 - x)^8.

%F From _Colin Barker_, Nov 11 2017: (Start)

%F a(n) = (25200 - 52056*n + 48650*n^2 - 20881*n^3 + 4340*n^4 - 154*n^5 - 70*n^6 + 11*n^7) / 5040 for n>0.

%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

%F (End)

%p -(4*x^8-2*x^7-17*x^6+25*x^5-43*x^4+38*x^3-22*x^2+7*x-1)/((x-1)^8)   ;

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

%p gfun[seriestolist](%) ;

%o (PARI) Vec((1 - 7*x + 22*x^2 - 38*x^3 + 43*x^4 - 25*x^5 + 17*x^6 + 2*x^7 - 4*x^8) / (1 - x)^8 + O(x^40)) \\ _Colin Barker_, Nov 11 2017

%K nonn,easy

%O 0,3

%A _R. J. Mathar_, Nov 08 2017