OFFSET
0,2
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 a path is defined to be the number of its steps.
Row n has ceiling(n/2) terms (n >= 1).
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)=1 because we have UUUDLD.
Triangle starts:
1;
1;
3;
9, 1;
28, 8;
90, 46, 1;
297, 231, 15;
MAPLE
eq:=t*z^2*G^3-(t-1)*z^2*G^2-(1-3*z+2*z^2)*G+(1-z)^2=0: G:=RootOf(eq, G): Gser:=simplify(series(G, z=0, 17)): for n from 0 to 14 do P[n]:=sort(coeff(Gser, z, n)) od: for n from 0 to 14 do seq(coeff(P[n], t, j), j=0..floor((n-1)/2)) od; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Emeric Deutsch, Mar 31 2007
STATUS
approved