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

0,3

Comments

A permutation is said to be Grassmannian if it has at most one descent. The definition for sigma is a pattern of size 9 with exactly one descent. For example, sigma can be chosen to be 124793568, 248135679, 367912458, 591234678, etc.

Links

Table of n, a(n) for n=0..36.

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).

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

Mathematica

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

Crossrefs

Cf. A000325, A362195.

Sequence in context: A362194 A111000 A362195 * A328882 A362197 A000325

Adjacent sequences: A362193 A362194 A362195 * A362197 A362198 A362199

Keyword

nonn,easy

Author

Jessica A. Tomasko, Apr 20 2023

Status

approved