|
Search: id:A128714
|
|
|
| A128714 |
|
Number of skew Dyck paths of semilength n ending with a left step. 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. |
|
+0
3
|
|
| 0, 0, 1, 4, 15, 58, 232, 954, 4010, 17156, 74469, 327168, 1452075, 6501156, 29326743, 133166064, 608188737, 2791992736, 12876049123, 59626721244, 277150709717, 1292583258866, 6046985696778, 28369001791034, 133436435891480
(list; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
COMMENT
|
Number of skew Dyck paths of semilength n and ending with a down step is A033321(n).
|
|
REFERENCES
|
E. Deutsch, E. Munarini and S. Rinaldi, Skew Dyck paths (in preparation).
|
|
FORMULA
|
G.f.=[1-3z-sqrt(1-6z+5z^2)]/[1+z+sqrt(1-6z+5z^2)]. G.f.=z(g-1)/(1-zg), where g=1+zg^2+z(g-1)=[1-z-sqrt(1-6z+5z^2)](2z).
|
|
EXAMPLE
|
a(3)=4 because we have UDUUDL, UUDUDL, UUUDDL and UUUDLL.
|
|
MAPLE
|
G:=(1-3*z-sqrt(1-6*z+5*z^2))/(1+z+sqrt(1-6*z+5*z^2)): Gser:=series(G, z=0, 30): seq(coeff(Gser, z, n), n=0..27);
|
|
CROSSREFS
|
Cf. A033321.
Sequence in context: A003126 A160156 A102052 this_sequence A007342 A017951 A129155
Adjacent sequences: A128711 A128712 A128713 this_sequence A128715 A128716 A128717
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 30 2007
|
|
|
Search completed in 0.002 seconds
|
