A226431 The number of permutations of length n in a particular geometric grid class.

1, 2, 6, 21, 73, 244, 786, 2458, 7510, 22527, 66579, 194408, 561988, 1610900, 4584426, 12966225, 36476173, 102132412, 284785878, 791182318, 2190833086, 6048706947, 16655647911, 45752451536, 125405039368, 343040546984, 936651104466, 2553146783253, 6948573570145

Offset: 1

Author

Jay Pantone, Jun 06 2013

Keywords

• nonn

Comments

This geometric grid class is given by the array [[0,0,1,0],[0,0,0,1],[0,1,-1,0],[1,0,0,-1]]. A picture is given in the LINKS section.

The simple permutations in this class are A226432.

Links

• Jay Pantone, The Enumeration of Permutations Avoiding 3124 and 4312, arXiv:1309.0832 [math.CO], 2013-2015.
• Jay Pantone, Picture of the geometric grid class
• Index entries for linear recurrences with constant coefficients, signature (9,-31,51,-41,15,-2).

Programs

Mathematica

LinearRecurrence[{9, -31, 51, -41, 15, -2}, {1, 2, 6, 21, 73, 244}, 29] (* Jean-François Alcover, Oct 30 2018 *)

PARI

x=x='x+O('x^66); Vec((x-7*x^2+19*x^3-22*x^4+9*x^5-x^6)/((1-x)*(1-2*x)*(1-3*x+x^2)^2) ) \\ Joerg Arndt, Jun 19 2013

Formula

G.f.: x*(1-7*x+19*x^2-22*x^3+9*x^4-x^5)/((1-x)*(1-2*x)*(1-3*x+x^2)^2).

a(n) = 3*A001871(n-1)-A001871(n) +2*A001906(n) +2^(n-1)+1. - R. J. Mathar, Aug 31 2013