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A191792 Number of length n left factors of Dyck paths having no UDUD's; here U=(1,1) and D=(1,-1). 1
1, 1, 2, 3, 5, 8, 15, 25, 46, 79, 147, 256, 477, 841, 1570, 2791, 5217, 9336, 17467, 31421, 58830, 106279, 199103, 360960, 676545, 1230185, 2306642, 4204931, 7887045, 14409480, 27035135, 49487641, 92872062, 170289575, 319647235, 586983680, 1102027213, 2026422689, 3805138290 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) = A191791(n,0).

LINKS

Table of n, a(n) for n=0..38.

FORMULA

G.f.: g(z)=C/(1-z*C), where C=C(z) is given by z^2*(1+z^2)*C^2-(1+z^2+z^4)*C+1+z^2=0.

EXAMPLE

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

MAPLE

eq := z^2*(1+z^2)*C^2-(1+z^2+z^4)*C+1+z^2 = 0: C := RootOf(eq, C): g := C/(1-z*C): gser := series(g, z = 0, 42): seq(coeff(gser, z, n), n = 0 .. 38);

CROSSREFS

Cf. A191791.

Sequence in context: A066372 A058519 A181065 * A151518 A082095 A177486

Adjacent sequences:  A191789 A191790 A191791 * A191793 A191794 A191795

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Jun 18 2011

STATUS

approved

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Last modified December 7 19:05 EST 2016. Contains 278895 sequences.