

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
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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/(12*z+z^4+sqrt(14*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/(12*z+z^4+sqrt(14*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/(12x+x^4+Sqrt[14x^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



