A361276 - OEIS

A361276

Number of 2413-avoiding even Grassmannian permutations of size n.

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

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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

Table of n, a(n) for n=0..49.

Juan B. Gil and Jessica A. Tomasko, Pattern-avoiding even and odd Grassmannian permutations, arXiv:2207.12617 [math.CO], 2022.

Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

FORMULA

G.f.: -(x^5-2*x^4-4*x^3+2*x^2+x-1)/((x+1)^2*(x-1)^4).

EXAMPLE