A226431 -id:A226431 - cp's OEIS frontend

A226432 The number of simple permutations of length n in a particular geometric grid class.

1, 2, 0, 2, 3, 7, 13, 25, 46, 84, 151, 269, 475, 833, 1452, 2518, 4347, 7475, 12809, 21881, 37274, 63336, 107375, 181657, 306743, 517057, 870168, 1462250, 2453811, 4112479, 6884101, 11510809, 19226950, 32084028, 53489287, 89097893, 148290067, 246615425, 409835844, 680609086

Offset: 1

Jay Pantone, Jun 06 2013

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 sequence of all permutations in this class is given by A226431.

Jay Pantone, The Enumeration of Permutations Avoiding 3124 and 4312, arXiv:1309.0832 [math.CO], (2013).
Jay Pantone, Picture of the geometric grid class
Index entries for linear recurrences with constant coefficients, signature (2,1,-2,-1).

Join[{1, 2}, LinearRecurrence[{2, 1, -2, -1}, {0, 2, 3, 7}, 40]] (* Jean-François Alcover, Jul 21 2018 *)

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

G.f.: x+2*x^2+ x^4*(1-x)*(2+x)/(1-x-x^2)^2 (corrected, Joerg Arndt, Jun 26 2013)

a(n) = A191830(n+2)-A000045(n+2), n>=4. - R. J. Mathar, Aug 31 2013

cp's OEIS Frontend

A226432 The number of simple permutations of length n in a particular geometric grid class.

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