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A116850 Number of permutations of length n which avoid the patterns 231, 12354.

%I A116850 #12 Oct 30 2017 12:48:17
%S A116850 1,2,5,14,41,119,334,902,2351,5945,14660,35408,84061,196715,454778,
%T A116850 1040522,2359451,5308589,11862208,26345684,58196201,127926527,
%U A116850 279970070,610271534,1325400391,2868904289,6190793084,13321109912,28588376501,61203284435,130728067570
%N A116850 Number of permutations of length n which avoid the patterns 231, 12354.
%C A116850 Inverse binomial transform (offset 0) is: 0, 1, 0, 2, 2, 6, 7, 12, 14, 20, 23, 30, 34, 42, 47, 56, 62, 72,.. with difference pattern +1, -1, +2, +0, +4, +1, +5, +2, +6, +3,... as in A168230. - _R. J. Mathar_, Feb 23 2013
%H A116850 Colin Barker, <a href="/A116850/b116850.txt">Table of n, a(n) for n = 1..1000</a>
%H A116850 Lara Pudwell, <a href="http://faculty.valpo.edu/lpudwell/maple/webbook/bookmain.html">Systematic Studies in Pattern Avoidance</a>, 2005.
%H A116850 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (9,-33,63,-66,36,-8).
%F A116850 G.f.: x*(1 - 7*x + 20*x^2 - 28*x^3 + 20*x^4 - 7*x^5) / ((1 - x)^3*(1 - 2*x)^3).
%F A116850 From _Colin Barker_, Oct 30 2017: (Start)
%F A116850 a(n) = (1/16)*(32-9*2^(1+n) + (8+2^n)*n + (8+2^n)*n^2).
%F A116850 a(n) = 9*a(n-1) - 33*a(n-2) + 63*a(n-3) - 66*a(n-4) + 36*a(n-5) - 8*a(n-6) for n>6.
%F A116850 (End)
%o A116850 (PARI) Vec(x*(1 - 7*x + 20*x^2 - 28*x^3 + 20*x^4 - 7*x^5) / ((1 - x)^3*(1 - 2*x)^3) + O(x^40)) \\ _Colin Barker_, Oct 30 2017
%K A116850 nonn,easy
%O A116850 1,2
%A A116850 _Lara Pudwell_, Feb 26 2006