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
Offset: 0
Examples
For n=4 the a(4) = 6 permutations are 1234, 1342, 1423, 2314, 3124, 3412.
Links
- 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).
Crossrefs
Programs
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Mathematica
LinearRecurrence[{2,1,-4,1,2,-1},{1,1,1,3,6,13},50] (* Harvey P. Dale, Aug 14 2023 *)
Formula
G.f.: -(x^5-2*x^4-4*x^3+2*x^2+x-1)/((x+1)^2*(x-1)^4).
Comments