A274376 Number of modified skew Dyck paths such that the area between the x-axis and the path is n.

1, 1, 1, 1, 2, 3, 5, 8, 12, 20, 32, 52, 84, 135, 219, 353, 572, 924, 1495, 2419, 3912, 6331, 10240, 16570, 26807, 43374, 70178, 113546, 183721, 297258, 480974, 778220, 1259184, 2037389, 3296554, 5333923, 8630446, 13964340, 22594740, 36559034, 59153708, 95712668

Offset: 0

Author

Alois P. Heinz, Jun 19 2016

Keywords

• nonn

Comments

A modified skew Dyck path is a path in the first quadrant which begins at the origin, ends on the x-axis, consists of steps U=(1,1) (up), D=(1,-1) (down) and A=(-1,1) (anti-down) so that A and D steps do not overlap.

Examples

			               /\    /\
a(5) = 3:   /\/  \  /  \/\  /\/\/\/\/\  .
.
            /\
            \ \    /\          /\          /\
a(6) = 5:   /  \  /  \/\/\  /\/  \/\  /\/\/  \  /\/\/\/\/\/\  .
		

Crossrefs

Column sums of A274372.

Cf. A230823.

Formula

a(n) = Sum_{k=0..n} A274372(k,n).