A329673 Number of meanders of length n with Motzkin-steps avoiding the consecutive steps HH.

1, 2, 4, 10, 24, 60, 152, 388, 1000, 2592, 6752, 17664, 46368, 122080, 322240, 852464, 2259552, 5999552, 15954560, 42486592, 113282048, 302386304, 807999744, 2161077120, 5785032448, 15498450944, 41551965184, 111478804480, 299274439680, 803905119232, 2160632498176, 5810087371520

Offset: 0

Author

Valerie Roitner, Nov 26 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(2)=4 since we have 4 meanders of length 2 avoiding HH, namely UU, UH, UD and HU.
		

Crossrefs

Cf. A104545 which counts excursions avoiding consecutive HH steps. Cf. A329672 and A329674 which count meanders avoiding consecutive UU and DD respectively.

Formula

G.f.: -(1-2*t-2*t^2-sqrt(1-4*t^2-8*t^3-4*t^4))/(2*t*(1-2*t-2*t^2)).

D-finite with recurrence (n+1)*a(n) -2*a(n-1) -4*n*a(n-2) +8*(-n+2)*a(n-3) +4*(-n+3)*a(n-4)=0. - R. J. Mathar, Jan 25 2023