|
Search: id:A121532
|
|
|
| A121532 |
|
Number of double rises at an even level in all nondecreasing Dyck paths of semilength n. A nondecreasing Dyck path is a Dyck path for which the sequence of the altitudes of the valleys is nondecreasing. |
|
+0
3
|
|
| 0, 0, 1, 6, 24, 87, 290, 926, 2861, 8640, 25634, 75015, 217100, 622620, 1772097, 5011394, 14093980, 39448623, 109954398, 305344314, 845165725, 2332485420, 6420202246, 17629525871, 48304680504, 132092031672, 360557665825
(list; graph; listen)
|
|
|
OFFSET
|
1,4
|
|
|
COMMENT
|
a(n)=Sum(k*A121531(n,k), k>=0). a(n)+A121530(n)=A054444(n-2).
|
|
REFERENCES
|
E. Barcucci, A. Del Lungo, S. Fezzi and R. Pinzani, Nondecreasing Dyck paths and q-Fibonacci numbers, Discrete Math., 170, 1997, 211-217.
|
|
FORMULA
|
G.f.=z^3*(1-3z^2+2z^3-z^4)/[(1+z)(1-3z+z^2)^2/(1-z-z^2)].
|
|
EXAMPLE
|
a(3)=1 because we have UDUDUD, UDUUDD, UUDDUD, UUDUDD, and UU/UDDD, the double rises at an odd level being indicated by a / (U=(1,1), D=(1,-1)).
|
|
MAPLE
|
g:=z^3*(1-3*z^2+2*z^3-z^4)/(1+z)/(1-3*z+z^2)^2/(1-z-z^2): gser:=series(g, z=0, 35): seq(coeff(gser, z, n), n=1..32);
|
|
CROSSREFS
|
Cf. A121530, A121531, A054444.
Sequence in context: A052150 A118043 A124807 this_sequence A025472 A002919 A006780
Adjacent sequences: A121529 A121530 A121531 this_sequence A121533 A121534 A121535
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 05 2006
|
|
|
Search completed in 0.002 seconds
|
