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A089354
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Number of generalized {(1,2),(1,-1)}-Dyck paths of length 3n with no peaks at level 2.
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0
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1, 0, 1, 4, 19, 96, 508, 2780, 15607, 89392, 520337, 3069232, 18305876, 110214144, 668950744, 4088824140, 25146253311, 155491812384, 966142729939, 6029139839684, 37771401328459, 237467581184384, 1497754198565104
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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FORMULA
| a(n)=(2/n)sum((-2)^i*(i+1)binomial(3n+1, n-2-i), i=0..n-2), n>=1. G.f.=g/(1+zg^2), where g=1+zg^3, g(0)=1. Also g=2sin(arcsin(3sqrt(3z)/2)/3)/sqrt(3z).
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EXAMPLE
| a(3)=4 because we have UUDUDDDDD, UUUDDDDDD, UUDDUDDDD and UUDDDUDDD, where
U=(1,2) and D=(1,-1).
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CROSSREFS
| Sequence in context: A020060 A122394 A047781 * A083315 A025573 A006194
Adjacent sequences: A089351 A089352 A089353 * A089355 A089356 A089357
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 26 2003
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