A329665 Number of meanders of length n with Motzkin-steps avoiding the consecutive steps UD, HH and DU.

1, 2, 3, 6, 11, 20, 38, 72, 136, 260, 499, 958, 1847, 3572, 6917, 13422, 26097, 50808, 99049, 193354, 377857, 739148, 1447292, 2836316, 5562774, 10918180, 21444029, 42143986, 82874681, 163060540, 320996342, 632211192, 1245727488, 2455674532, 4842782497, 9554018554, 18855375593, 37224944572

Offset: 0

Author

Valerie Roitner, Nov 19 2019

Keywords

• nonn
• walk

Comments

The Motzkin step set is U=(1,1), H=(1,0) and D=(1,-1). A meander is a path starting at (0,0) and never crossing the x-axis, i.e., staying at nonnegative altitude.

Examples

			a(3)=6 as one has 6 meanders of length 3, namely: UUU, UUH, UHU, UHD, HUU, HUH.
		

Crossrefs

Cf. A308435 (avoiding UD and DU), A329666 (avoiding UU and HH).

Cf. A329664.

Formula

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