A060148 Number of closed forest meander systems with 2n crossings.

1, 1, 3, 15, 97, 733, 6147, 55541, 530773, 5298723, 54780831, 582817337, 6350647873, 70614662303, 798935833885, 9176290300419, 106793746090045, 1257408517909283, 14958873368871405, 179614516459970349, 2174717049372338913, 26530091641879493297, 325875790867387681293

Offset

0,3

Comments

A forest meander system is a meander system that does not have any components which are entirely enclosed by another. - Andrew Howroyd, Nov 22 2015

The components of a forest meander system do not necessarily all have exterior arches. See example. Those that do are called tame (A060066). - Andrew Howroyd, Feb 02 2025

Links

Table of n, a(n) for n=0..22.

Roland Bacher, Meander algebras

Formula

1 <= A060066(n) <= a(n) <= A060174(n) <= A060198(n) <= 16^n. - Andrew Howroyd, Feb 02 2025

Example

An example of a 2 component forest meander system with 8 crossings that is not tame:
      ________
     / ______ \
    / /      \ \
   / / /\  /\ \ \
   \ \ \/ / /  \/
    \ \__/ /
     \____/

Crossrefs

Row sums of A380368.

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

Sequence in context: A231445 A378882 A108442 * A143435 A331325 A132437

Adjacent sequences: A060145 A060146 A060147 * A060149 A060150 A060151

Keyword

nonn,nice,changed

Author

N. J. A. Sloane, Apr 10 2001

Extensions

More terms from Sascha Kurz, Mar 25 2002

a(15)-a(20) from Andrew Howroyd, Nov 22 2015

a(0)=1 prepended and a(21)-a(22) from Andrew Howroyd, Jan 31 2025

Status

approved