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A167635 Number of Dyck paths of semilength n, having no ascents and no descents of length 1, and having no peaks at odd level. 2
1, 0, 1, 0, 2, 0, 5, 1, 14, 7, 43, 36, 143, 166, 509, 731, 1915, 3158, 7523, 13560, 30537, 58257, 127029, 251266, 538253, 1089666, 2313121, 4754148, 10051130, 20868070, 44065633, 92132176, 194617333, 408971295, 864899013, 1824485600, 3864369141 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

a(n)=A167634(n,0).

LINKS

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

FORMULA

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

EXAMPLE

a(6)=5 because we have UUDDUUDDUUDD, UUDDUUUUDDDD, UUUUDDDDUUDD, UUUUDDUUDDDD, and UUUUUUDDDDDD.

MAPLE

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

CROSSREFS

Cf. A167634, A167638

Sequence in context: A243998 A290395 A082974 * A192426 A075603 A264357

Adjacent sequences:  A167632 A167633 A167634 * A167636 A167637 A167638

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Nov 08 2009

STATUS

approved

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Last modified October 23 23:05 EDT 2021. Contains 348217 sequences. (Running on oeis4.)