|
Search: id:A128743
|
|
|
| A128743 |
|
Number of UU's (i.e. doublerises) in all skew Dyck paths of semilength n. 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. |
|
+0
2
|
|
| 0, 0, 2, 13, 69, 346, 1700, 8286, 40264, 195488, 949302, 4613025, 22436997, 109240038, 532410060, 2597468685, 12684628125, 62002335160, 303332650190, 1485213237135, 7277719953415, 35687662907750, 175120787451540
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
a(n)=Sum[k*A128718(n,k), k=0..n-1].
|
|
REFERENCES
|
E. Deutsch, E. Munarini and S. Rinaldi, Skew Dyck paths (in preparation).
|
|
FORMULA
|
G.f.=[1-4z+z^2+(z-1)sqrt(1-6z+5z^2)]/[2z*sqrt(1-6z+5z^2)].
|
|
EXAMPLE
|
a(2)=2 because the paths of semilength 2 are UDUD, UUDD and UUDL, having altogether 2 UU's.
|
|
MAPLE
|
G:=(1-4*z+z^2+(z-1)*sqrt(1-6*z+5*z^2))/2/z/sqrt(1-6*z+5*z^2): Gser:=series(G, z=0, 30): seq(coeff(Gser, z, n), n=0..25);
|
|
CROSSREFS
|
Cf. A128718.
Sequence in context: A038144 A097977 A136780 this_sequence A097349 A109112 A163190
Adjacent sequences: A128740 A128741 A128742 this_sequence A128744 A128745 A128746
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 30 2007
|
|
|
Search completed in 0.002 seconds
|
