OFFSET
3,1
COMMENTS
Conjecture: a(n) is the number of linear intervals in the tilting posets of type D_n. An interval is linear if it is isomorphic to a total order. The conjecture has been checked up to the term 187187 for n = 9.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 3..1659
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[(9/4 # - 51/8 - 5/8/(2 # - 3) + 1/# + 6/(# + 1))*Binomial[2 # - 2, # - 1] &, 21, 3] (* Michael De Vlieger, Jan 17 2024 *)
PROG
(Sage)
def a(n):
return (9/4*n-51/8-5/8/(2*n-3)+1/n+6/(n+1))*binomial(2*n-2, n-1)
(PARI) a(n) = (9*n/4-51/8-5/(16*n-24)+1/n+6/(n+1))*binomial(2*n-2, n-1) \\ Felix Fröhlich, May 27 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
F. Chapoton, May 27 2021
STATUS
approved