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
Keywords
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
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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
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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