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A361270
Number of 1324-avoiding odd Grassmannian permutations of size n.
3
0, 0, 1, 2, 5, 8, 16, 20, 38, 40, 75, 70, 131, 112, 210, 168, 316, 240, 453, 330, 625, 440, 836, 572, 1090, 728, 1391, 910, 1743, 1120, 2150, 1360, 2616, 1632, 3145, 1938, 3741, 2280, 4408, 2660, 5150, 3080, 5971, 3542, 6875, 4048, 7866, 4600, 8948, 5200, 10125
OFFSET
0,4
COMMENTS
A permutation is said to be Grassmannian if it has at most one descent. A permutation is odd if it has an odd number of inversions.
LINKS
Juan B. Gil and Jessica A. Tomasko, Pattern-avoiding even and odd Grassmannian permutations, arXiv:2207.12617 [math.CO], 2022.
FORMULA
G.f.: x^2*(2*x^4+x^2+2*x+1)/((1+x)^4*(1-x)^4).
EXAMPLE
For n=4 the a(4)=5 permutations are 1243, 2134, 2341, 2413, 4123.
PROG
(PARI) Vec(x^2*(2*x^4+x^2+2*x+1)/((1+x)^4*(1-x)^4)+O(x^50)) \\ _Michel Marcus_, Mar 07 2023
CROSSREFS
Sequence in context: A186413 A080084 A065093 * A360671 A168470 A295998
KEYWORD
nonn,easy
AUTHOR
_Juan B. Gil_, Mar 07 2023
STATUS
approved