A060198 Dimensions of graded algebra associated with forest meanders.

1, 16, 240, 3552, 52224, 764672, 11163936, 162631712, 2365037376, 34344187424, 498139336992, 7217820903328, 104490673015136, 1511512136496064, 21849735526096256, 315654728421607968, 4557598148470097472, 65771755517857808768, 948727279133187672224, 13679121303056997294080, 197153311343380929158240

Offset: 0

Author

N. J. A. Sloane, Apr 10 2001

Keywords

• nonn

Comments

Number of meander slices with 2n crossings which can be open on both sides and whose loops are all even. A loop is even if it has its least point at an even index with crossings numbered from zero. This definition excludes slices such as (open, open, close, close) since the inner loop is not even. It also excludes (up, open, close, down) even though the loop is not contained in another. - Andrew Howroyd, Feb 07 2025

Examples

			a(1) = 240 = 256 - 16 = 4^4 - 4^2 counts all length 4 sequences of open, close, up and down steps, excluding those that have an open + close pair as the central two elements. - _Andrew Howroyd_, Feb 07 2025
		

Links

• Roland Bacher, Meander algebras, Institut Fourier, UMR 5582, Laboratoire de Mathématiques, 1999.

Crossrefs

Meander sequences in Bacher's paper: A005315, A060066, A060089, A060111, A060148, A060149, A060174, A060198, A060206.

Extensions

Offset corrected and a(7) onwards from Andrew Howroyd, Feb 06 2025