A116747 Number of permutations of length n which avoid the patterns 1234, 2413, 3241.

1, 2, 6, 21, 72, 230, 689, 1970, 5460, 14833, 39790, 105890, 280367, 739878, 1948186, 5121973, 13451620, 35299782, 92580429, 242705586, 636062896, 1666534337, 4365640346, 11434584546, 29946505947, 78421715110, 205352199014

Offset

1,2

Links

Table of n, a(n) for n=1..27.

D. Callan, T. Mansour, Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns, arXiv:1705.00933 (2017), Table 2 No 47.

Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.

Index entries for linear recurrences with constant coefficients, signature (9, -33, 64, -71, 45, -15, 2).

Formula

G.f.: A(x) = -{x(2x^6-12x^5+24x^4-31x^3+21x^2-7x+1)}/{(2x-1)(x^2-3x+1)(x-1)^4}

a(0)=1, a(1)=2, a(2)=6, a(3)=21, a(4)=72, a(5)=230, a(6)=689, a(n)= 9*a(n-1)-33*a(n-2)+64*a(n-3)-71*a(n-4)+45*a(n-5)-15*a(n-6)+2*a(n-7) [From Harvey P. Dale, May 19 2011]

Mathematica

LinearRecurrence[{9, -33, 64, -71, 45, -15, 2}, {1, 2, 6, 21, 72, 230, 689}, 40] (* or *) Rest[CoefficientList[Series[-(x(2x^6-12x^5+24x^4-31x^3+21x^2-7x+1))/ ((2x-1)(x^2-3x+1)(x-1)^4), {x, 0, 40}], x]] (* Harvey P. Dale, May 19 2011 *)

Crossrefs

Sequence in context: A116748 A116812 A116830 * A116810 A294703 A116800

Adjacent sequences: A116744 A116745 A116746 * A116748 A116749 A116750

Keyword

nonn,easy

Author

Lara Pudwell, Feb 26 2006

Status

approved