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A322507
a(n) is the number of arches for semi-meanders with n top arches that have exactly two covering arches.
0
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
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
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