A274054 Number of modified skew Dyck paths of semilength n such that the area between the x-axis and the path is n*(n+1)/2.

1, 1, 0, 1, 3, 6, 14, 40, 140, 422, 1346, 4487, 15234, 52632, 183913, 651948, 2336751, 8438406, 30712379, 112603500, 415459873, 1541646225, 5750112809, 21548036621, 81096740799, 306404247854, 1161863199131, 4420429256826, 16869986745367, 64567073382731

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(1) = 1:   /\
.
            /\
            \ \
a(3) = 1:   /  \
.
                /\                          /\
               /  \         /\/\/\         /  \
a(4) = 3:   /\/    \   ,   /      \   ,   /    \/\   .
		

Crossrefs

Cf. A000217, A230823, A274372.

Formula

a(n) = A274372(n,n*(n+1)/2) = A274372(n,A000217(n)).