A260696 The number of length-n permutations avoiding the patterns 1234, 1324, 1432 and 3214.

1, 1, 2, 6, 20, 62, 172, 471, 1337, 3846, 11030, 31442, 89470, 254934, 727203, 2074435, 5915652, 16866988, 48093810, 137141828, 391072846, 1115164897, 3179915535, 9067592160, 25856510664, 73730732368, 210245631360, 599521974384, 1709555338705, 4874850377793, 13900789573274, 39638539791222

Offset: 0

Author

Christian Bean, Nov 26 2015

Keywords

• nonn

Links

• C. Bean, M. Tannock and H. Ulfarsson, Pattern avoiding permutations and independent sets in graphs, arXiv:1512.08155 [math.CO], 2015.
• Index entries for linear recurrences with constant coefficients, signature (2,1,2,4,8,0,-15,-14,-7).

Crossrefs

Cf. A263790.

Programs

Magma

I:=[1,1,2,6,20,62,172,471,1337]; [n le 9 select I[n] else 2*Self(n-1)+Self(n-2)+2*Self(n-3)+4*Self(n-4)+8*Self(n-5)-15*Self(n-7)-14*Self(n-8)-7*Self(n-9): n in [1..35]]; // Vincenzo Librandi, Dec 31 2015

Mathematica

CoefficientList[Series[-(x^3 + x^2 + x - 1)/(7*x^9 + 14*x^8 + 15*x^7 - 8*x^5 - 4*x^4 - 2*x^3 - x^2 - 2*x + 1), {x, 0, 30}], x] (* Wesley Ivan Hurt, Dec 29 2015 *)
LinearRecurrence[{2, 1, 2, 4, 8, 0, -15, -14, -7}, {1, 1, 2, 6, 20, 62, 172, 471, 1337}, 40 ] (* Vincenzo Librandi, Dec 31 2015 *)

Formula

G.f.: -(x^3 + x^2 + x - 1)/(7*x^9 + 14*x^8 + 15*x^7 - 8*x^5 - 4*x^4 - 2*x^3 - x^2 - 2*x + 1).

a(n) = 2*a(n-1)+a(n-2)+2*a(n-3)+4*a(n-4)+8*a(n-5)-15*a(n-7)-14*a(n-8)-7*a(n-9) for n>8. - Wesley Ivan Hurt, Dec 29 2015