A337581 a(n) is the number of semi-meanders with n top arches that have both an arch of length 1 adjacent to the center of the top arch configuration and an arch of length 1 starting or ending the top arch configuration.

1, 2, 4, 8, 16, 40, 96, 264, 696, 2016, 5624, 16840, 48792, 149512, 445112, 1387384, 4215496, 13312752, 41097864, 131146520, 410045672, 1319612232, 4169110888, 13511677040, 43060097728, 140383359392

Offset

2,2

Comments

The number of semi-meanders with n top arches is A000682(n). The number of semi-meanders with n top arches that have a starting or ending arch of length 1 is 2*A000682(n-1). The number of semi-meanders with n top arches that have an arch adjacent to the center with length 1 is 2*A000682(n-1).

Links

Table of n, a(n) for n=2..27.

Formula

For n >= 4: a(n) = 4*A000682(n-2).

Example

For n = 5: (10) is a starting or ending arch of length 1, [10] is an arch adjacent to the center with length 1,  a(5) = 8.
(10)101[10]100, 110[10]010(10), (10)1[10]11000, 11100[10]0(10), (10)111[10]000,
111[10]000(10), (10)1[10]01100, 11001[10]0(10).
/\ = arch with length 1, (10) = arches with length 1 at ends or adjacent to center
        /\      /\                       /\
       /  \    /  \                     /  \
      / /\ \  / /\ \  /\               /    \
      1 10 0  1(10) 0(10)     /\  /\  / /\ /\\
         center|      end    (10) 10  1(10)100
                             end center|

Crossrefs

Cf. A000682.

Sequence in context: A028497 A197244 A350495 * A259377 A275071 A018575

Adjacent sequences: A337578 A337579 A337580 * A337582 A337583 A337584

Keyword

nonn,more

Author

Roger Ford, Sep 01 2020

Status

approved