A322507 a(n) is the number of arches for semi-meanders with n top arches that have exactly two covering arches.

0, 0, 0, 2, 6, 28, 82, 310, 918, 3246, 9762, 33586, 102490, 348220, 1076238, 3635050, 11358178, 38261430, 120676406, 406137648, 1291309912, 4345989212, 13914717064, 46856195890

Offset: 1

Author

Roger Ford, Dec 12 2018

Keywords

• nonn
• more

Examples

			Example: semi-meanders  n=4, -- top arches with two covering arches
                  /\                    /\
       /\        //\\     /\           //\\
/\ /\ //\\,  /\ ///\\\,  //\\ /\ /\,  ///\\\ /\
                  --                    --          a(4) = 2.
		

Crossrefs

Cf. A259689.

Formula

a(n) = Sum_{k=3..floor((n+4)/2)} (A259689(n+2,k)*(k-2)) - Sum_{k=2..floor((n+2)/2)} (A259689(n,k)*k*(k-1)).

Extensions

Offset changed to 1 and a(14)-a(24) from Jinyuan Wang, Aug 02 2021