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A274376
Number of modified skew Dyck paths such that the area between the x-axis and the path is n.
1
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.
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 19 2016
STATUS
approved