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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.

%I A362193 #29 Apr 14 2023 03:34:26
%S A362193 1,1,2,5,12,27,57,113,211,373,628,1013,1574,2367,3459,4929,6869,9385,
%T A362193 12598,16645,21680,27875,35421,44529,55431,68381,83656,101557,122410,
%U A362193 146567,174407,206337,242793,284241,331178,384133,443668,510379,584897
%N 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.
%C A362193 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.
%H A362193 Juan B. Gil and Jessica A. Tomasko, <a href="https://doi.org/10.54550/ECA2022V2S4PP6">Restricted Grassmannian permutations</a>, Enum. Combin. Appl. 2 (2022), no. 4, Article #S4PP6.
%H A362193 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A362193 a(n) = 1 + Sum_{i=2..5} binomial(n,i).
%F A362193 G.f.: (1-5*x+11*x^2-12*x^3+7*x^4-x^5)/(1-x)^6.
%F A362193 a(0) = 1; a(1) = 1; a(n) = 1 + A027660(n-2), n >= 2. - _Omar E. Pol_, Apr 12 2023
%p A362193 a:= n-> 1+(n-1)*n*(n+1)*(n*(n-5)+26)/120:
%p A362193 seq(a(n), n=0..38);  # _Alois P. Heinz_, Apr 12 2023
%t A362193 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 *)
%o A362193 (PARI) a(n) = 1 + sum(i=3, 6, binomial(n, i-1)) \\ _Andrew Howroyd_, Apr 10 2023
%Y A362193 Cf. A027660, A361270, A361271, A356185, A000325, A027927.
%K A362193 nonn,easy
%O A362193 0,3
%A A362193 _Jessica A. Tomasko_, Apr 10 2023