OFFSET
0,2
COMMENTS
The number of bigrassmannian permutations in the type B hyperoctahedral group of order 2^n*n!, i.e., those with a unique left and right type B descent or the identity. This can be characterized by avoiding 18 signed permutation patterns.
LINKS
Joshua Swanson, Bigrassmannians and pattern avoidance notes.
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = (1/24)*(n^4 + 10*n^3 + 11*n^2 + 2*n + 24).
G.f.: (x^4 - 5x^3 + 7x^2 - 3x + 1)/(1-x)^5.
E.g.f.: exp(x)*(24 + 24*x + 48*x^2 + 16*x^3 + x^4)/24. - Stefano Spezia, Jan 09 2024
EXAMPLE
For n=2, all eight 2 X 2 signed permutation matrices are bigrassmannian except the negative of the identity matrix, or equivalently the one with window notation [-1 -2], so a(2) = 7.
MATHEMATICA
Table[Binomial[n + 3, 4] + Binomial[n + 1, 3] + 1, {n, 0, 20}]
PROG
(Python)
def A368881(n): return 1+(n*(n*(n*(n + 10) + 11) + 2))//24 # Chai Wah Wu, Jan 27 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Joshua Swanson, Jan 08 2024
STATUS
approved