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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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%I #13 May 07 2023 06:30:42

%S 1,1,2,5,12,27,58,121,248,503,1013,2025,4005,7801,14899,27809,50627,

%T 89829,155364,262125,431890,695839,1097768,1698137,2579106,3850731,

%U 5658511,8192497,11698195,16489517,22964057,31620993,43081941,58115113,77663158,102875093

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

%C 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.

%H J. B. Gil and J. Tomasko, <a href="https://doi.org/10.54550/ECA2022V2S4PP6">Restricted Grassmannian permutations</a>, ECA 2:4 (2022) Article S4PP6.

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

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

%F 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.

%Y Cf. A000325, A362196.

%K nonn,easy

%O 0,3

%A _Jessica A. Tomasko_, Apr 29 2023