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

1,3

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Cf. A000682.

Sequence in context: A261492 A027056 A024428 * A049075 A318797 A318850

Adjacent sequences: A330266 A330267 A330268 * A330270 A330271 A330272

Keyword

nonn

Author

Roger Ford, Dec 07 2019

Extensions

More terms from Jinyuan Wang, Dec 08 2019

Status

approved