|
Search: id:A128096
|
|
|
| A128096 |
|
Number of steps that touch the x-axis in all peakless Motzkin paths of length n. |
|
+0
2
|
|
| 1, 2, 5, 12, 27, 62, 144, 336, 790, 1870, 4452, 10656, 25629, 61910, 150145, 365450, 892434, 2185928, 5369097, 13221422, 32634935, 80730942, 200116410, 496992992, 1236482727, 3081389406, 7690966549, 19224282880, 48119034729, 120599916654
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
a(n)=Sum(k*A128095(n,k), k=1..n).
|
|
FORMULA
|
G.f.=4[1-z^2-sqrt((1+z+z^2)(1-3z+z^2))]/[1-z+z^2+sqrt((1+z+z^2)(1-3z+z^2))]^2.
|
|
EXAMPLE
|
a(3)=5 because in the peakless Motzkin paths of length 3 (namely HHH and UHD, where H=(1,0), U=(1,1), and D=(1,-1)) all the steps, with the exception of H in UHD, touch the x-axis.
|
|
MAPLE
|
g:=4*(1-z^2-sqrt((1+z+z^2)*(1-3*z+z^2)))/(1-z+z^2+sqrt((1+z+z^2)*(1-3*z+z^2)))^2: gser:=series(g, z=0, 38): seq(coeff(gser, z, n), n=1..35);
|
|
CROSSREFS
|
Cf. A128095.
Sequence in context: A091596 A077863 A018009 this_sequence A018010 A026710 A118898
Adjacent sequences: A128093 A128094 A128095 this_sequence A128097 A128098 A128099
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 14 2007
|
|
|
Search completed in 0.002 seconds
|
