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A361276
Number of 2413-avoiding even Grassmannian permutations of size n.
0
1, 1, 1, 3, 6, 13, 22, 37, 55, 81, 111, 151, 196, 253, 316, 393, 477, 577, 685, 811, 946, 1101, 1266, 1453, 1651, 1873, 2107, 2367, 2640, 2941, 3256, 3601, 3961, 4353, 4761, 5203, 5662, 6157, 6670, 7221, 7791, 8401, 9031, 9703, 10396, 11133, 11892, 12697, 13525, 14401
OFFSET
0,4
COMMENTS
A permutation is said to be Grassmannian if it has at most one descent. A permutation is even if it has an even 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^5-2*x^4-4*x^3+2*x^2+x-1)/((x+1)^2*(x-1)^4).
EXAMPLE
For n=4 the a(4) = 6 permutations are 1234, 1342, 1423, 2314, 3124, 3412.
MATHEMATICA
LinearRecurrence[{2, 1, -4, 1, 2, -1}, {1, 1, 1, 3, 6, 13}, 50] (* _Harvey P. Dale_, Aug 14 2023 *)
CROSSREFS
For the corresponding odd permutations, cf. A006918.
Sequence in context: A019079 A280029 A178097 * A211870 A239987 A048134
KEYWORD
nonn,easy
AUTHOR
_Juan B. Gil_, Mar 10 2023
STATUS
approved