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

1,2

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

Table of n, a(n) for n=1..29.

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).

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

Mathematica

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

Prog

(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

Crossrefs

Sequence in context: A165521 A294696 A116784 * A116802 A294697 A116826

Adjacent sequences: A226428 A226429 A226430 * A226432 A226433 A226434

Keyword

nonn

Author

Jay Pantone, Jun 06 2013

Status

approved