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

0,2

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

Links

Table of n, a(n) for n=0..20.

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

Example

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

Crossrefs

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

Sequence in context: A227440 A103975 A162791 * A097829 A010559 A342884

Adjacent sequences: A060195 A060196 A060197 * A060199 A060200 A060201

Keyword

nonn

Author

N. J. A. Sloane, Apr 10 2001

Extensions

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

Status

approved