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

Author

Peter Luschny, Nov 14 2018

Keywords

• nonn

Comments

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

Links

• 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.

Crossrefs

Cf. A321396.

Programs

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 *)

Formula

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