|
| |
|
|
A191796
|
|
Number of DUU's in all length n left factors of Dyck paths; here U=(1,1) and D=(1,-1).
|
|
1
|
|
|
|
0, 0, 0, 0, 1, 3, 9, 21, 52, 113, 261, 550, 1226, 2542, 5546, 11389, 24494, 49989, 106413, 216258, 456826, 925586, 1943550, 3929090, 8210896, 16571018, 34494114, 69523116, 144246532, 290424604, 600907508, 1208835421, 2495229602, 5016122029, 10332784253, 20759855626
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,6
|
|
|
COMMENTS
|
a(n) = Sum(k*A191795(n,k), k>=0).
|
|
|
LINKS
|
Table of n, a(n) for n=0..35.
|
|
|
FORMULA
|
G.f.: g(z)=((1-3*z^2-z^3)*sqrt(1-4*z^2) -1+5*z^2+z^3-4*z^4)/(2*z*(1-2*z)*sqrt(1-4*z^2)).
|
|
|
EXAMPLE
|
a(4)=1 because in UDUD, U(DUU), UUDD, UUDU, UUUD, and UUUU the total number of DUUs is 0 + 1 + 0 + 0 +0 + 0 = 1 (shown between parentheses).
|
|
|
MAPLE
|
g := (((1-3*z^2-z^3)*sqrt(1-4*z^2)-1+5*z^2+z^3-4*z^4)*1/2)/(z*(1-2*z)*sqrt(1-4*z^2)): gser := series(g, z = 0, 40): seq(coeff(gser, z, n), n = 0 .. 35);
|
|
|
CROSSREFS
|
Cf. A191795.
Sequence in context: A111209 A109755 A005254 * A007056 A026551 A060578
Adjacent sequences: A191793 A191794 A191795 * A191797 A191798 A191799
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Emeric Deutsch, Jun 18 2011
|
|
|
STATUS
|
approved
|
| |
|
|
