A334498 Number of intervals in Fang's Schroeder-Tamari poset.

2, 8, 46, 320, 2500, 21120, 188758, 1760256, 16969756, 168022016, 1700483916, 17527963648, 183499999368, 1946861076480, 20896083575142, 226570927865856, 2478789884919084, 27336509563600896, 303635676268456996, 3394385993908879360, 38168423356190965688, 431472747874361540608

Offset

1,1

Comments

Fang (2020), Theorem 4.2, gives a generating function.

References

Wenjie Fang, A partial order on Motzkin paths, Discrete Math., 343 (2020), #111802. See Section 4.

Links

Table of n, a(n) for n=1..22.

Wenjie Fang, A partial order on Motzkin paths, arXiv preprint arXiv:1801.04809 [math.CO], 2018.

Formula

a(n) ~ sqrt(5/9 + 1/sqrt(3)) * (4*sqrt(45 + 26*sqrt(3))/3)^n / (sqrt(Pi)*n^(5/2)). - Vaclav Kotesovec, May 07 2020

Mathematica

Rest[CoefficientList[Series[(-1 + w^4*x^2 + w*(1 + 2*x) - w^3*(3*x + 2*x^2)) / (w*x*(-1 + w^2*x)) /. w -> Root[-1 + #1 + 2*x*#1^2 - 2*x*#1^3 - x*(1 + x)*#1^4 + x^2*#1^5 &, 1], {x, 0, 30}], x]] (* Vaclav Kotesovec, May 07 2020 *)

Crossrefs

Cf. A307787.

Sequence in context: A266507 A202081 A258315 * A006664 A276367 A326351

Adjacent sequences: A334495 A334496 A334497 * A334499 A334500 A334501

Keyword

nonn

Author

N. J. A. Sloane, May 07 2020

Extensions

More terms from Vaclav Kotesovec, May 07 2020

Status

approved