A300952 Number of Dyck paths of semilength n having equal areas above the path and below the path, measured within the smallest enclosing rectangle based on the x-axis.

1, 1, 2, 2, 7, 7, 35, 43, 238, 341, 1981, 3030, 18649, 29597, 190809, 311294, 2072334, 3462486, 23551368, 40166551, 277378932, 481159175, 3362641488, 5912848608, 41749776145, 74210799645, 528856595713, 948300730648, 6814672450367, 12308638880274, 89116042070616

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..51

Wikipedia, Counting lattice paths

Example

                                                                  .__________.
                        a(5) = 7:                                 |    /\    |
           .______________________________________________________|   /  \   |
           |  /\/\    |  /\      |    /\    |      /\  |    /\/\  |  /    \  |
.__________| /    \   | /  \/\/\ | /\/  \/\ | /\/\/  \ |   /    \ | /      \ |
|/\/\/\/\/\|/______\/\|/________\|/________\|/________\|/\/______\|/________\| .

Crossrefs

Column k=0 of A300953.

Cf. A000108, A300323.

Sequence in context: A271229 A199886 A117779 * A195326 A263868 A263793

Adjacent sequences: A300949 A300950 A300951 * A300953 A300954 A300955

Keyword

nonn

Author

Alois P. Heinz, Mar 16 2018

Status

approved