

A274405


Number of antidown steps in all modified skew Dyck paths of semilength n.


2



0, 0, 0, 1, 6, 34, 179, 915, 4607, 22988, 114090, 564359, 2785921, 13735074, 67665208, 333211828, 1640575047, 8077199130, 39770520844, 195852723348, 964689515033, 4752800817185, 23422061819883, 115456855588378, 569293729146929, 2807864888917275
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OFFSET

0,5


COMMENTS

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


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..500


FORMULA

a(n) = Sum_{k>0} k * A274404(n,k).
a(n) ~ c * 5^n / sqrt(n), where c = 0.0554525135364274199547478570703521322323... .  Vaclav Kotesovec, Jun 26 2016


MAPLE

b:= proc(x, y, t, n) option remember; `if`(y>n, 0, `if`(n=y,
`if`(t=2, 0, [1, 0]), b(x+1, y+1, 0, n1)+`if`(t<>1
and x>0, (p> p+[0, p[1]])(b(x1, y+1, 2, n1)), 0)+
`if`(t<>2 and y>0, b(x+1, y1, 1, n1), 0)))
end:
a:= n> b(0$3, 2*n)[2]:
seq(a(n), n=0..30);


CROSSREFS

Cf. A230823, A274404.
Sequence in context: A304944 A266359 A198765 * A144142 A126643 A320745
Adjacent sequences: A274402 A274403 A274404 * A274406 A274407 A274408


KEYWORD

nonn


AUTHOR

Alois P. Heinz, Jun 20 2016


STATUS

approved



