A362196 Number of Grassmannian permutations of size n that avoid a pattern, sigma, where sigma is a pattern of size 9 with exactly one descent.

1, 1, 2, 5, 12, 27, 58, 121, 248, 502, 1003, 1970, 3785, 7086, 12897, 22804, 39187, 65519, 106744, 169747, 263930, 401909, 600348, 880947, 1271602, 1807756, 2533961, 3505672, 4791295, 6474512, 8656907, 11460918, 15033141, 19548013, 25211902, 32267633, 40999480

Offset: 0

Author

Jessica A. Tomasko, Apr 20 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 9 with exactly one descent. For example, sigma can be chosen to be 124793568, 248135679, 367912458, 591234678, etc.

Links

• Juan B. Gil and Jessica Tomasko, Restricted Grassmannian permutations, ECA 2:4 (2022) Article S4PP6.
• Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Crossrefs

Cf. A000325, A362195.

Programs

Mathematica

Table[1 + Sum[Binomial[n, i-1],{i,3,9}],{n,0,36}] (* Stefano Spezia, Apr 20 2023 *)

Formula

a(n) = 1 + Sum_{i=2..8} binomial(n,i).

G.f.: (1-8*x+29*x^2-61*x^3+81*x^4-69*x^5+37*x^6-11*x^7+2*x^8)/(1-x)^9.

a(n) = (n^8-20*n^7+210*n^6-1064*n^5+3969*n^4-4340*n^3+15980*n^2-14736*n+40320)/8!. - Alois P. Heinz, Apr 21 2023