A263790 The number of length-n permutations avoiding the patterns 1234, 1324 and 2143.

1, 1, 2, 6, 21, 75, 268, 958, 3425, 12245, 43778, 156514, 559565, 2000543, 7152292, 25570698, 91419729, 326841561, 1168515890, 4177649198, 14935828405, 53398205443, 190907947468, 682529386598, 2440162233937, 8724007852045, 31189857766034, 111509210441322, 398664979703373

Offset: 0

Author

Christian Bean, Nov 23 2015

Keywords

• nonn
• easy

Links

• C. Bean, M. Tannock and H. Ulfarsson, Pattern avoiding permutations and independent sets in graphs, arXiv:1512.08155 [math.CO], 2015, eq. (4).
• D. Callan, T. Mansour, Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns, arXiv:1705.00933 [math.CO] (2017), Table 2 No 181.
• Index entries for linear recurrences with constant coefficients, signature (4,-2,2,-1).

Programs

Magma

I:=[1,1,2,6]; [n le 4 select I[n] else 4*Self(n-1)-2*Self(n-2)+2*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Jan 01 2016

Maple

t1:=(1-3*x-2*x^3)/(1-4*x+2*x^2-2*x^3+x^4);
series(t1,x,40);
seriestolist(%); # N. J. A. Sloane, Nov 09 2016

Mathematica

LinearRecurrence[{4, -2, 2, -1}, {1, 1, 2, 6}, 30] (* Jean-François Alcover, Dec 31 2015 *)
CoefficientList[Series[(2 x^3 + 3 x - 1)/(-x^4 + 2*x^3 - 2 x^2 + 4 x - 1), {x, 0, 35}], x] (* Vincenzo Librandi, Jan 01 2016 *)

PARI

Vec((2*x^3 + 3*x - 1)/(-x^4 + 2*x^3 - 2*x^2 + 4*x - 1) + O(x^50)) \\ Michel Marcus, Nov 23 2015

Formula

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