A362196 -id:A362196 - cp's OEIS frontend

A362197 Number of Grassmannian permutations of size n that avoid a pattern, sigma, where sigma is a pattern of size 10 with exactly one descent.

1, 1, 2, 5, 12, 27, 58, 121, 248, 503, 1013, 2025, 4005, 7801, 14899, 27809, 50627, 89829, 155364, 262125, 431890, 695839, 1097768, 1698137, 2579106, 3850731, 5658511, 8192497, 11698195, 16489517, 22964057, 31620993, 43081941, 58115113, 77663158, 102875093

Offset: 0

Jessica A. Tomasko, Apr 29 2023

A permutation is said to be Grassmannian if it has at most one descent. The definition for sigma is a pattern of size 10 with exactly one descent. For example, sigma can be chosen to be 124789356(10), 247913568(10), 36(10)1245789, 57(10)1234689, etc.

J. B. Gil and J. Tomasko, Restricted Grassmannian permutations, ECA 2:4 (2022) Article S4PP6.
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Cf. A000325, A362196.

a(n) = 1 + Sum_{i=2..9} binomial(n,i).

G.f.: (1-9*x+37*x^2-90*x^3+142*x^4-150*x^5+106*x^6-48*x^7+13*x^8-x^9)/(1-x)^10.

cp's OEIS Frontend

A362197 Number of Grassmannian permutations of size n that avoid a pattern, sigma, where sigma is a pattern of size 10 with exactly one descent.

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