A344717 a(n) = (3n - 9/2 - 1/n + 6/(n+1))*binomial(2n-2,n-1).

6, 34, 169, 791, 3576, 15807, 68783, 295867, 1261468, 5341128, 22487906, 94244294, 393439840, 1637091585, 6792664635, 28115240595, 116120791380, 478689505140, 1969993524510, 8095052323410, 33218808108720, 136148925337230, 557389537873974, 2279607910207326

Offset: 2

Author

F. Chapoton, May 27 2021

Keywords

• nonn

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.

Crossrefs

For the tilting posets of type A, see A344136.

For the Cambrian lattices of types A, B and D, see A344136, A344228, A344321.

For similar sequences, see A344191, A344216.

Programs

Mathematica

Array[(3 # - 9/2 - 1/# + 6/(# + 1))*Binomial[2 # - 2, # - 1] &, 24, 2] (* Michael De Vlieger, Jan 17 2024, after Sage *)

Sage

def a(n):
    return (3*n-9/2-1/n+6/(n+1))*binomial(2*n-2,n-1)