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%I #16 Oct 30 2018 04:26:25
%S 1,2,6,19,56,157,428,1149,3058,8097,21370,56279,147990,388727,1020252,
%T 2676139,7016372,18389377,48184544,126229809,330635974,865940277,
%U 2267709166,5938235819,15549095466,40713244907,106599027888,279100615999,730736374568,1913175616597
%N The number of permutations of length n in a particular geometric grid class.
%C This geometric grid class is given by the array [[0,1,0],[0,0,*],[1,-1,0]]. A picture is given in the LINKS section.
%H Jay Pantone, <a href="https://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="/A226433/a226433.png">Picture of the geometric grid class</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (7,-18,21,-11,2)
%F 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)).
%F a(n) = 2*A001519(n)-2^(n-2)-n+1, n>1. - _R. J. Mathar_, Aug 31 2013
%t Join[{1}, LinearRecurrence[{7, -18, 21, -11, 2}, {2, 6, 19, 56, 157}, 29]] (* _Jean-François Alcover_, Oct 30 2018 *)
%o (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
%K nonn
%O 1,2
%A _Jay Pantone_, Jun 06 2013
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