login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A089380 Number of Motzkin paths of length n with no UD, UHD, UHHD, UHHHD, ..., starting at level zero (here H=(1,0), U=(1,1), D=(1,-1)). 1
1, 1, 1, 1, 2, 6, 18, 50, 133, 349, 919, 2443, 6559, 17759, 48417, 132765, 365883, 1012827, 2814975, 7852359, 21977172, 61697208, 173688720, 490222392, 1386896799, 3932313671, 11172152779, 31801604227, 90683754826, 259017103918 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..29.

FORMULA

G.f.=2(1-z)/[1-2z+3z^2+(1-z)sqrt(1-2z-3z^2)].

EXAMPLE

a(5)=6 because among the 21 Motzkin paths of length 5 only the following have

no U(H^p)D for any p>=0: HHHHH, HUUDD, UUDDH, UHUDD, UUDHD and UUHDD.

CROSSREFS

Cf. A001006.

Sequence in context: A258625 A062026 A048495 * A271897 A304962 A180282

Adjacent sequences:  A089377 A089378 A089379 * A089381 A089382 A089383

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Dec 27 2003

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 11 01:52 EDT 2021. Contains 342886 sequences. (Running on oeis4.)