OFFSET
2,1
COMMENTS
Conjecture: These are the number of linear intervals in the tilting posets of type B_n. An interval is linear if it is isomorphic to a total order. The conjecture has been checked up to the term 295867 for n = 9.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 2..1658
Clément Chenevière, Enumerative study of intervals in lattices of Tamari type, Ph. D. thesis, Univ. Strasbourg (France), Ruhr-Univ. Bochum (Germany), HAL tel-04255439 [math.CO], 2024. See p. 152.
MATHEMATICA
Array[(3 # - 9/2 - 1/# + 6/(# + 1))*Binomial[2 # - 2, # - 1] &, 24, 2] (* Michael De Vlieger, Jan 17 2024, after Sage *)
PROG
(Sage)
def a(n):
return (3*n-9/2-1/n+6/(n+1))*binomial(2*n-2, n-1)
CROSSREFS
For the tilting posets of type A, see A344136.
KEYWORD
nonn
AUTHOR
F. Chapoton, May 27 2021
STATUS
approved