A362193 Number of Grassmannian permutations of size n that avoid a pattern, sigma, where sigma is a pattern of size 6 with exactly one descent.

1, 1, 2, 5, 12, 27, 57, 113, 211, 373, 628, 1013, 1574, 2367, 3459, 4929, 6869, 9385, 12598, 16645, 21680, 27875, 35421, 44529, 55431, 68381, 83656, 101557, 122410, 146567, 174407, 206337, 242793, 284241, 331178, 384133, 443668, 510379, 584897

Offset: 0

Author

Jessica A. Tomasko, Apr 10 2023

Keywords

• nonn
• easy

Comments

A permutation is said to be Grassmannian if it has at most one descent. The definition for sigma is a pattern of size 6 with exactly one descent. For example, sigma can be chosen to be 124356, 241356, 361245, 512346, etc.

Links

• Juan B. Gil and Jessica A. Tomasko, Restricted Grassmannian permutations, Enum. Combin. Appl. 2 (2022), no. 4, Article #S4PP6.
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Cf. A027660, A361270, A361271, A356185, A000325, A027927.

Programs

Maple

a:= n-> 1+(n-1)*n*(n+1)*(n*(n-5)+26)/120:
seq(a(n), n=0..38);  # Alois P. Heinz, Apr 12 2023

Mathematica

CoefficientList[Series[(1 - 5 x + 11 x^2 - 12 x^3 + 7 x^4 - x^5)/(1 - x)^6, {x, 0, 38}], x] (* Michael De Vlieger, Apr 12 2023 *)

PARI

a(n) = 1 + sum(i=3, 6, binomial(n, i-1)) \\ Andrew Howroyd, Apr 10 2023

Formula

a(n) = 1 + Sum_{i=2..5} binomial(n,i).

G.f.: (1-5*x+11*x^2-12*x^3+7*x^4-x^5)/(1-x)^6.

a(0) = 1; a(1) = 1; a(n) = 1 + A027660(n-2), n >= 2. - Omar E. Pol, Apr 12 2023