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A167638 Number of Dyck paths of semilength n, having no ascents and no descents of length 1, and having no peaks at even level. 2
1, 0, 0, 1, 0, 2, 1, 5, 5, 15, 21, 51, 85, 188, 344, 730, 1407, 2935, 5831, 12094, 24480, 50754, 103995, 216043, 446447, 930206, 1934328, 4043275, 8448882, 17716170, 37166403, 78163336, 164520540, 346935912, 732317063, 1548096255, 3275859473 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

a(n)=A167637(n,0).

LINKS

Table of n, a(n) for n=0..36.

FORMULA

G.f.: G(z) = [1 + 2z - z^3 - sqrt(1 - 4z^2 - 2z^3 + z^6)]/[2z(1 + z )].

EXAMPLE

a(5)=2 because we have UUUDDUUDDD and UUUUUDDDDD.

MAPLE

G := ((1+2*z-z^3-sqrt(1-4*z^2-2*z^3+z^6))*1/2)/(z*(1+z)): Gser := series(G, z = 0, 40): seq(coeff(Gser, z, n), n = 0 .. 38);

CROSSREFS

Cf. A167637, A167635

Sequence in context: A128731 A129157 A086905 * A209108 A269019 A184234

Adjacent sequences:  A167635 A167636 A167637 * A167639 A167640 A167641

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Nov 08 2009

STATUS

approved

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Last modified December 8 04:27 EST 2016. Contains 278902 sequences.