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

1,4

Links

Table of n, a(n) for n=1..24.

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)).

Example

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

Crossrefs

Cf. A259689.

Sequence in context: A115156 A370749 A185072 * A340471 A242511 A360035

Adjacent sequences: A322504 A322505 A322506 * A322508 A322509 A322510

Keyword

nonn,more

Author

Roger Ford, Dec 12 2018

Extensions

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

Status

approved