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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, 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
0,5
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.
FORMULA
a(n) = A274372(n,n*(n+1)/2) = A274372(n,A000217(n)).
EXAMPLE
a(1) = 1: /\
.
/\
\ \
a(3) = 1: / \
.
/\ /\
/ \ /\/\/\ / \
a(4) = 3: /\/ \ , / \ , / \/\ .
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 19 2016
STATUS
approved