A226433 The number of permutations of length n in a particular geometric grid class.

1, 2, 6, 19, 56, 157, 428, 1149, 3058, 8097, 21370, 56279, 147990, 388727, 1020252, 2676139, 7016372, 18389377, 48184544, 126229809, 330635974, 865940277, 2267709166, 5938235819, 15549095466, 40713244907, 106599027888, 279100615999, 730736374568, 1913175616597

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..30.

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 (7,-18,21,-11,2)

Formula

G.f.: x*(1-5*x+10*x^2-8*x^3+x^5)/((1-x)^2*(1-2*x)*(1-3*x+x^2)).

a(n) = 2*A001519(n)-2^(n-2)-n+1, n>1. - R. J. Mathar, Aug 31 2013

Mathematica

Join[{1}, LinearRecurrence[{7, -18, 21, -11, 2}, {2, 6, 19, 56, 157}, 29]] (* Jean-François Alcover, Oct 30 2018 *)

Prog

(PARI) x='x+O('x^66); Vec((x-5*x^2+10*x^3-8*x^4+x^6)/((1-x)^2*(1-2*x)*(1-3*x+x^2))) \\ Joerg Arndt, Jun 19 2013

Crossrefs

Sequence in context: A027098 A183305 A192715 * A121483 A077834 A325918

Adjacent sequences: A226430 A226431 A226432 * A226434 A226435 A226436

Keyword

nonn

Author

Jay Pantone, Jun 06 2013

Status

approved