A330269 The number of semi-meanders with n top arches and concentric arches within the starting arch or a starting arch with length one.

1, 1, 2, 4, 8, 18, 42, 108, 282, 786, 2192, 6402, 18600, 55978, 167256, 514102, 1567976, 4896164, 15170630, 47957260, 150468678, 480371736, 1522649458, 4900568718, 15665593150, 50761432998, 163431901126, 532624603680, 1725349278270, 5650796083020, 18401781369182

Offset: 1

Author

Roger Ford, Dec 07 2019

Keywords

• nonn

Examples

			For n = 5, a(5) = 8:
        /\                                  /\
       //\\                      /\        /  \          /\
      ///\\\      /\  /\        /  \      /  /\\    /\  //\\
   /\////\\\\, /\//\\//\\, /\/\//\/\\, /\//\//\\\, //\\///\\\,
                              /\
                 /\          //\\          starting arch
    /\  /\      //\\  /\    ///\\\        (1) (2) (3) (4)
   //\\//\\/\, ///\\\//\\, ////\\\\/\,     4 + 2 + 1 + 1 = 8.
		

Links

• Jean-François Alcover, Table of n, a(n) for n = 1..46

Crossrefs

Cf. A000682.

Programs

Mathematica

A000136 = Import["https://oeis.org/A000136/b000136.txt", "Table"][[All, 2]];
a[n_] := If[n == 1, 1, Sum[A000136[[k]]/k, {k, 1, n - 1}]];
a /@ Range[46] (* Jean-François Alcover, Feb 13 2020 *)

Formula

a(1) = 1, for n >= 2, a(n) = Sum_{k=1..n-1} A000682(k).

Extensions

More terms from Jinyuan Wang, Dec 08 2019