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A111283
Number of permutations avoiding the patterns {4321, 45132, 45231, 35412, 53412, 45213, 43512, 45312, 456123, 451623, 356124}; number of strong sorting class based on 4321.
0
1, 1, 2, 6, 23, 96, 409, 1751, 7505, 32176, 137956, 591501, 2536132, 10873981, 46623553, 199904321, 857114814, 3674987126, 15756967635, 67559972476, 289671844661, 1242004318751, 5325249092137, 22832672531956, 97897943538708
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) + a(n-2) + a(n-3) - 4; n>=4.
G.f.: 1+x*(1-3*x-x^2-x^3)/((1-x)*(1-4*x-x^2-x^3)). - Colin Barker, Jan 16 2012
MATHEMATICA
a[1] = 1; a[2] = 2; a[3] = 6; a[n_] := a[n] = 4a[n - 1] + a[n - 2] + a[n - 3] - 4; Table[a[n], {n, 24}] (* Robert G. Wilson v, Nov 04 2005 *)
LinearRecurrence[{5, -3, 0, -1}, {1, 2, 6, 23}, 30] (* Harvey P. Dale, Jan 01 2017 *)
CROSSREFS
Sequence in context: A150295 A150296 A134064 * A150297 A374165 A150298
KEYWORD
nonn
AUTHOR
Len Smiley, Nov 01 2005
EXTENSIONS
More terms from Robert G. Wilson v, Nov 04 2005
a(0)=1 prepended by Alois P. Heinz, Mar 12 2024
STATUS
approved