OFFSET

0,3

COMMENTS

A 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 L=(-1,-1)(left) so that up and left steps do not overlap. The length of the path is defined to be the number of its steps.

Row n has n-1 terms (n >= 2).

Row sums yield A002212.

LINKS

E. Deutsch, E. Munarini, S. Rinaldi, Skew Dyck paths, J. Stat. Plann. Infer. 140 (8) (2010) 2191-2203

FORMULA

EXAMPLE

T(3,1)=4 because we have UUUDDD, UUUDLD, UUUDDL and UUUDLL.

Triangle starts:

1;

1;

3;

6, 4;

16, 12, 8;

40, 53, 28, 16;

MAPLE

eq:=z*(t+z-t*z)*G^2-(1-z-z^2+t*z^2)*G+1-t*z=0: G:=RootOf(eq, G): Gser:=simplify(series(G, z=0, 14)): for n from 0 to 12 do P[n]:=sort(coeff(Gser, z, n)) od: 1; 1; for n from 2 to 11 do seq(coeff(P[n], t, j), j=0..n-2) od; # yields sequence in triangular form

CROSSREFS

KEYWORD

nonn,tabf

AUTHOR

Emeric Deutsch, Mar 30 2007

STATUS

approved