|
|
A226432
|
|
The number of simple permutations of length n in a particular geometric grid class.
|
|
4
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
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.
|
|
LINKS
|
|
|
FORMULA
|
G.f.: x+2*x^2+ x^4*(1-x)*(2+x)/(1-x-x^2)^2 (corrected, Joerg Arndt, Jun 26 2013)
|
|
MATHEMATICA
|
Join[{1, 2}, LinearRecurrence[{2, 1, -2, -1}, {0, 2, 3, 7}, 40]] (* Jean-François Alcover, Jul 21 2018 *)
|
|
PROG
|
(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
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|