A362195 Number of Grassmannian permutations of size n that avoid a pattern, sigma, where sigma is a pattern of size 8 with exactly one descent.
1, 1, 2, 5, 12, 27, 58, 121, 247, 493, 958, 1805, 3290, 5799, 9894, 16369, 26317, 41209, 62986, 94165, 137960, 198419, 280578, 390633, 536131, 726181, 971686, 1285597, 1683190, 2182367, 2803982, 3572193, 4514841, 5663857, 7055698, 8731813, 10739140, 13130635
Offset: 0
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 (8,-28,56,-70,56,-28,8,-1).
Programs
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Mathematica
Table[1 + Sum[Binomial[n, i-1],{i,3,8}],{n,0,37}] (* Stefano Spezia, Apr 20 2023 *)
Formula
a(n) = 1 + Sum_{i=3..8} binomial(n, i-1).
G.f.: (1-7*x+22*x^2-39*x^3+42*x^4-27*x^5+10*x^6-x^7)/(1-x)^8.
Comments