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A111285 Number of permutations avoiding the patterns {2431, 3421, 4231, 4321, 24513, 42513, 34512, 43512}; number of strong sorting class based on 2431.

%I A111285 #33 Mar 12 2024 08:50:49
%S A111285 1,1,2,6,20,66,216,706,2308,7546,24672,80666,263740,862306,2819336,
%T A111285 9217906,30138228,98537866,322172592,1053353226,3443970860,
%U A111285 11260168946,36815469656,120369313506,393551182948,1286727730586,4206996000512
%N A111285 Number of permutations avoiding the patterns {2431, 3421, 4231, 4321, 24513, 42513, 34512, 43512}; number of strong sorting class based on 2431.
%H A111285 Vincenzo Librandi, <a href="/A111285/b111285.txt">Table of n, a(n) for n = 0..1000</a>
%H A111285 M. Albert, R. Aldred, M. Atkinson, C Handley, D. Holton, D. McCaughan and H. van Ditmarsch, <a href="https://doi.org/10.37236/1928">Sorting Classes</a>, Elec. J. of Comb., Vol. 12 (2005), R31.
%H A111285 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3,2).
%F A111285 a(n) = 4*a(n-1) - 3*a(n-2) + 2*a(n-3), n>=4.
%F A111285 G.f.: 1+x*(1-x)^2/(1-4*x+3*x^2-2*x^3).
%F A111285 a(n) = A175005(n)+A175005(n-2)-2*A175005(n-1). - _R. J. Mathar_, Aug 19 2022~
%t A111285 a[1] = 1; a[2] = 2; a[3] = 6; a[n_] := a[n] = 4a[n - 1] - 3a[n - 2] + 2a[n - 3]; Table[a[n], {n, 26}] (* _Robert G. Wilson v_ *)
%t A111285 CoefficientList[Series[(1-2*x+x^2)/(1-4*x+3*x^2-2*x^3),{x,0,40}],x] (* or *) LinearRecurrence[{4,-3,2},{1,2,6},40] (* _Vincenzo Librandi_, Jun 27 2012 *)
%o A111285 (Magma) I:=[1, 2, 6]; [n le 3 select I[n] else 4*Self(n-1)-3*Self(n-2)+2*Self(n-3): n in [1..30]]; // _Vincenzo Librandi_, Jun 27 2012
%K A111285 nonn,easy
%O A111285 0,3
%A A111285 _Len Smiley_, Nov 01 2005
%E A111285 a(0)=1 prepended by _Alois P. Heinz_, Mar 12 2024