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The number of simple permutations of length n in a particular geometric grid class.
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%I #20 Jul 21 2018 10:05:07

%S 1,2,0,2,3,7,13,25,46,84,151,269,475,833,1452,2518,4347,7475,12809,

%T 21881,37274,63336,107375,181657,306743,517057,870168,1462250,2453811,

%U 4112479,6884101,11510809,19226950,32084028,53489287,89097893,148290067,246615425,409835844,680609086

%N The number of simple 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 sequence of all permutations in this class is given by A226431.

%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).

%H Jay Pantone, <a href="/A226432/a226432.png">Picture of the geometric grid class</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-2,-1).

%F G.f.: x+2*x^2+ x^4*(1-x)*(2+x)/(1-x-x^2)^2 (corrected, _Joerg Arndt_, Jun 26 2013)

%F a(n) = A191830(n+2)-A000045(n+2), n>=4. - _R. J. Mathar_, Aug 31 2013

%t Join[{1, 2}, LinearRecurrence[{2, 1, -2, -1}, {0, 2, 3, 7}, 40]] (* _Jean-François Alcover_, Jul 21 2018 *)

%o (PARI) x='x+O('x^66); Vec(x+2*x^2+(x^4*(1-x)*(2+x))/((1-x-x^2)^2) ) \\ _Joerg Arndt_, Jun 19 2013

%K nonn,easy

%O 1,2

%A _Jay Pantone_, Jun 06 2013