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 6 with exactly one descent. For example, sigma can be chosen to be 124356, 241356, 361245, 512346, etc.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1000
Juan B. Gil and Jessica A. Tomasko, Restricted Grassmannian permutations, Enum. Combin. Appl. 2 (2022), no. 4, Article #S4PP6.
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
a(n) = 1 + Sum_{i=2..5} binomial(n,i).
G.f.: (1-5*x+11*x^2-12*x^3+7*x^4-x^5)/(1-x)^6.
a(0) = 1; a(1) = 1; a(n) = 1 + A027660(n-2), n >= 2. - Omar E. Pol, Apr 12 2023
MAPLE
a:= n-> 1+(n-1)*n*(n+1)*(n*(n-5)+26)/120:
seq(a(n), n=0..38); # Alois P. Heinz, Apr 12 2023
MATHEMATICA
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 *)
PROG
(PARI) a(n) = 1 + sum(i=3, 6, binomial(n, i-1)) \\ Andrew Howroyd, Apr 10 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jessica A. Tomasko, Apr 10 2023
STATUS
approved