login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A191794 Number of length n left factors of Dyck paths having no UUDD's; here U=(1,1) and D=(1,-1). 1
1, 1, 2, 3, 5, 8, 14, 23, 41, 69, 124, 212, 383, 662, 1200, 2091, 3799, 6661, 12122, 21359, 38919, 68850, 125578, 222892, 406865, 724175, 1322772, 2360010, 4313155, 7711148, 14099524, 25252819, 46192483, 82863807, 151628090, 272385447, 498578411, 896774552 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) = A191793(n,0).

LINKS

Table of n, a(n) for n=0..37.

FORMULA

G.f.: g(z) = 2/(1-2*z+z^4+sqrt(1-4*z^2+2*z^4+z^8)).

EXAMPLE

a(4)=5 because we have UDUU, UDUD, UUDU, UUUD, and UUUU, where U=(1,1) and D=(1,-1) (the path UUDD does not qualify).

MAPLE

g := 2/(1-2*z+z^4+sqrt(1-4*z^2+2*z^4+z^8)): gser := series(g, z = 0, 42): seq(coeff(gser, z, n), n = 0 .. 37);

MATHEMATICA

CoefficientList[Series[2/(1-2x+x^4+Sqrt[1-4x^2+2x^4+x^8]), {x, 0, 40}], x] (* Harvey P. Dale, Jun 19 2011 *)

CROSSREFS

Cf. A191793.

Sequence in context: A039828 A246360 A005627 * A191388 A194850 A062692

Adjacent sequences:  A191791 A191792 A191793 * A191795 A191796 A191797

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Jun 18 2011

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 December 6 06:34 EST 2019. Contains 329784 sequences. (Running on oeis4.)