|
| |
|
|
A129166
|
|
Number of skew Dyck paths of semilength n with no base pyramids. 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. A pyramid in a skew Dyck word (path) is a factor of the form u^h d^h, h being the height of the pyramid. A base pyramid is a pyramid starting on the x-axis.
|
|
1
| |
|
|
1, 0, 1, 5, 19, 73, 292, 1203, 5065, 21697, 94274, 414514, 1840981, 8247011, 37220261, 169079113, 772489020, 3547371679, 16364309243, 75799327800, 352402156770, 1643878188646, 7691841654538, 36091803172733
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,4
|
|
|
COMMENTS
| a(n)=A129165(n,0).
|
|
|
LINKS
| E. Deutsch, E. Munarini, S. Rinaldi, Skew Dyck paths, J. Stat. Plann. Infer. 140 (8) (2010) 2191-2203
|
|
|
FORMULA
| G.f.=(1-z)[3-3z-sqrt(1-6z+5z^2)]/[2-(1-z)[1-z-sqrt(1-6z+5z^2)]].
|
|
|
EXAMPLE
| a(2)=1 because we have UUDL.
|
|
|
MAPLE
| G:=(1-z)*(3-3*z-sqrt(1-6*z+5*z^2))/(2-(1-z)*(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. A129165.
Sequence in context: A086386 A047155 A034548 * A149763 A149764 A149765
Adjacent sequences: A129163 A129164 A129165 * A129167 A129168 A129169
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 04 2007
|
| |
|
|
