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

Author

Roger Ford, Sep 01 2020

Keywords

• nonn
• more

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).

Examples

			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.

Formula

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