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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.
2
1, 1, 2, 6, 20, 66, 216, 706, 2308, 7546, 24672, 80666, 263740, 862306, 2819336, 9217906, 30138228, 98537866, 322172592, 1053353226, 3443970860, 11260168946, 36815469656, 120369313506, 393551182948, 1286727730586, 4206996000512
OFFSET
0,3
LINKS
M. Albert, R. Aldred, M. Atkinson, C Handley, D. Holton, D. McCaughan and H. van Ditmarsch, Sorting Classes, Elec. J. of Comb., Vol. 12 (2005), R31.
FORMULA
a(n) = 4*a(n-1) - 3*a(n-2) + 2*a(n-3), n>=4.
G.f.: 1+x*(1-x)^2/(1-4*x+3*x^2-2*x^3).
a(n) = A175005(n)+A175005(n-2)-2*A175005(n-1). - R. J. Mathar, Aug 19 2022~
MATHEMATICA
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 *)
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 *)
PROG
(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
CROSSREFS
Sequence in context: A083323 A174846 A369431 * A052991 A246019 A226510
KEYWORD
nonn,easy
AUTHOR
Len Smiley, Nov 01 2005
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Mar 12 2024
STATUS
approved