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A361274
Number of 1342-avoiding even Grassmannian permutations of size n.
3
1, 1, 1, 3, 5, 12, 17, 32, 41, 67, 81, 121, 141, 198, 225, 302, 337, 437, 481, 607, 661, 816, 881, 1068, 1145, 1367, 1457, 1717, 1821, 2122, 2241, 2586, 2721, 3113, 3265, 3707, 3877, 4372, 4561, 5112, 5321, 5931, 6161, 6833, 7085, 7822, 8097, 8902, 9201, 10077, 10401
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.
a(n) is also the number of 3124-avoiding even Grassmannian permutations of size n.
LINKS
Juan B. Gil and Jessica A. Tomasko, Pattern-avoiding even and odd Grassmannian permutations, arXiv:2207.12617 [math.CO], 2022.
FORMULA
G.f.: -(2*x^6-x^5-5*x^4-2*x^3+3*x^2-1)/((x+1)^3*(x-1)^4).
E.g.f.: ((24 - 9*x + 6*x^2 + 2*x^3)*cosh(x) + (33 - 6*x + 9*x^2 + 2*x^3)*sinh(x))/24. - _Stefano Spezia_, Mar 09 2023
EXAMPLE
For n=4 the a(4) = 5 permutations are 1234, 1423, 2314, 3124, 3412.
MATHEMATICA
LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {1, 1, 1, 3, 5, 12, 17}, 51] (* _Stefano Spezia_, Mar 09 2023 *)
CROSSREFS
Sequence in context: A203150 A237351 A299490 * A126471 A317100 A199932
KEYWORD
nonn,easy
AUTHOR
_Juan B. Gil_, Mar 09 2023
STATUS
approved