|
Search: id:A089164
|
|
|
| A089164 |
|
Number of steps in all Schroeder paths (i.e. consisting of steps U=(1,1), D=(1,-1),H=(2,0) and never going below the x-axis) from (0,0) to (2n,0). |
|
+0
1
|
|
| 3, 19, 107, 591, 3259, 18019, 99987, 556831, 3111347, 17436915, 97981179, 551871087, 3114878571, 17613879747, 99768824355, 565962587199, 3214923140707, 18284737574611, 104110467624075, 593397580894351
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
FORMULA
|
a(n)=(1/n)sum(k C(n, k-n)C(k, n-1), k=n..2n). G.f.=1/2-1/z+(2-7z+z^2)/[2z sqrt(1-6*z+z^2)].
|
|
EXAMPLE
|
a(2)=19 because the six Schroeder paths HH,HUD,UDH,UHD,UDUD,UUDD from (0,0) to (4,0) have 19 steps (i.e. letters) alltogether.
|
|
CROSSREFS
|
Cf. A006318.
Sequence in context: A047029 A095120 A151539 this_sequence A072950 A130425 A103005
Adjacent sequences: A089161 A089162 A089163 this_sequence A089165 A089166 A089167
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 06 2003
|
|
|
Search completed in 0.002 seconds
|
