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The number of permutations of length n in a particular geometric grid class.
2

%I #17 Oct 30 2018 04:26:33

%S 1,2,6,21,73,244,786,2458,7510,22527,66579,194408,561988,1610900,

%T 4584426,12966225,36476173,102132412,284785878,791182318,2190833086,

%U 6048706947,16655647911,45752451536,125405039368,343040546984,936651104466,2553146783253,6948573570145

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

%C 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.

%C The simple permutations in this class are A226432.

%H Jay Pantone, <a href="http://arxiv.org/abs/1309.0832">The Enumeration of Permutations Avoiding 3124 and 4312</a>, arXiv:1309.0832 [math.CO], 2013-2015.

%H Jay Pantone, <a href="/A226431/a226431.png">Picture of the geometric grid class</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (9,-31,51,-41,15,-2).

%F 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).

%F a(n) = 3*A001871(n-1)-A001871(n) +2*A001906(n) +2^(n-1)+1. - _R. J. Mathar_, Aug 31 2013

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

%o (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

%K nonn

%O 1,2

%A _Jay Pantone_, Jun 06 2013