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 8 with exactly one descent. For example, sigma can be chosen to be 12473568, 24781356, 36124578, 58123467, etc.
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).
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.
MATHEMATICA
Table[1 + Sum[Binomial[n, i-1], {i, 3, 8}], {n, 0, 37}] (* Stefano Spezia, Apr 20 2023 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jessica A. Tomasko, Apr 20 2023
STATUS
approved