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A362194

Number of Grassmannian permutations of size n that avoid a pattern, sigma, where sigma is a pattern of size 7 with exactly one descent.

1, 1, 2, 5, 12, 27, 58, 120, 239, 457, 838, 1475, 2498, 4083, 6462, 9934, 14877, 21761, 31162, 43777, 60440, 82139, 110034, 145476, 190027, 245481, 313886, 397567, 499150, 621587, 768182, 942618, 1148985, 1391809, 1676082, 2007293, 2391460, 2835163, 3345578, 3930512

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OFFSET

0,3

COMMENTS

A permutation is said to be Grassmannian if it has at most one descent. The definition for sigma is a pattern of size 7 with exactly one descent. For example, sigma can be chosen to be 1247356, 2413567, 3671245, 5712346, etc.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Juan B. Gil and Jessica Tomasko, Restricted Grassmannian permutations, ECA 2:4 (2022) Article S4PP6.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

FORMULA

a(n) = 1 + Sum_{i=2..6} binomial(n, i).

a(n) = A008859(n) - n.

G.f.: (1-6*x+16*x^2-23*x^3+19*x^4-8*x^5+2*x^6)/(1-x)^7.

E.g.f.: exp(x)*(720 + 360*x^2 + 120*x^3 + 30*x^4 + 6*x^5 + x^6)/720. - Stefano Spezia, Apr 20 2023

MATHEMATICA

A362194[n_]:= 1 + Sum[Binomial[n, i], {i, 2, 6}];

Array[A362194, 50, 0] (* Paolo Xausa, Jan 25 2026 *)