A321572 Related to the set of Motzkin trees where all leaves are at the same unary height 2.

0, 1, 0, 1, 1, 3, 2, 9, 7, 27, 25, 85, 86, 287, 296, 975, 1065, 3369, 3825, 11887, 13836, 42389, 50597, 152549, 186186, 554103, 688494, 2027304, 2559958, 7461971, 9561298, 27617581, 35846863, 102707431, 134874639, 383561963, 509090498, 1437822479, 1927045425

Offset

0,6

Comments

Row 2 of A321396, see section 3.2 in O. Bodini et al.

Links

Table of n, a(n) for n=0..38.

Olivier Bodini, Danièle Gardy, Bernhard Gittenberger, Zbigniew Gołębiewski, On the number of unary-binary tree-like structures with restrictions on the unary height, arXiv:1510.01167v1 [math.CO], 2015.

Formula

G.f.: (1 - sqrt(1 - 2*z + 2*z*sqrt(1 - 2*z + 2*z*sqrt(1 - 4*z^2))))/(2*z^3).

Maple

gf := -(sqrt(2*z*(sqrt(2*z*(sqrt(1-4*z^2)-1)+1)-1)+1)-1)/(2*z^3):
series(gf, z, 44): seq(coeff(%, z, n), n=0..38);

Mathematica

CoefficientList[(1 - Sqrt[2 Sqrt[2 Sqrt[1 - 4z^2] z - 2z + 1] z - 2z + 1])/ (2z^3) + O[z]^40, z] (* Jean-François Alcover, Jun 03 2019 *)

Crossrefs

Cf. A321396.

Sequence in context: A237651 A124003 A159588 * A118045 A276023 A268822

Adjacent sequences: A321569 A321570 A321571 * A321573 A321574 A321575

Keyword

nonn

Author

Peter Luschny, Nov 14 2018

Status

approved