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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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

M. Albert, R. Aldred, M. Atkinson, C Handley, D. Holton, D. McCaughan and H. van Ditmarsch, Sorting Classes, Elec. J. of Comb. 12 (2005)

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (4,-3,2).

FORMULA

a(n) = 4*a(n-1) - 3*a(n-2) + 2*a(n-3), n>=4.

G.f.: x*(1-2*x+x^2)/(1-4*x+3*x^2-2*x^3).

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: A096487 A083323 A174846 * A052991 A246019 A226510

Adjacent sequences:  A111282 A111283 A111284 * A111286 A111287 A111288

KEYWORD

nonn,easy

AUTHOR

Len Smiley, Nov 01 2005

STATUS

approved

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Last modified July 13 04:01 EDT 2020. Contains 335673 sequences. (Running on oeis4.)