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

0,5

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.

Links

Table of n, a(n) for n=0..41.

Formula

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

Example

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

Crossrefs

Column sums of A274372.

Cf. A230823.

Sequence in context: A013984 A107479 A117761 * A018149 A152909 A328597

Adjacent sequences: A274373 A274374 A274375 * A274377 A274378 A274379

Keyword

nonn

Author

Alois P. Heinz, Jun 19 2016

Status

approved