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A274405 Number of anti-down 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 (list; graph; refs; listen; history; text; internal format)
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

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, n-1)+`if`(t<>1

       and x>0, (p-> p+[0, p[1]])(b(x-1, y+1, 2, n-1)), 0)+

      `if`(t<>2 and y>0, b(x+1, y-1, 1, n-1), 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

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Last modified December 10 23:18 EST 2019. Contains 329910 sequences. (Running on oeis4.)