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Search: id:A162985
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| A162985 |
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Number of Dyck paths with no UUU's and no DDD's of semilength n and having no UUDUDD's (U=(1,1), D=(1,-1)). |
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+0
2
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| 1, 1, 2, 3, 6, 12, 25, 53, 114, 249, 550, 1227, 2760, 6253, 14256, 32682, 75293, 174224, 404741, 943622, 2207135, 5177817, 12179904, 28722736, 67890481, 160812128, 381671061, 907529504, 2161622683, 5157014539, 12321750366, 29482362166
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OFFSET
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0,3
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COMMENT
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a(n)=A162984(n,0).
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FORMULA
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G.f. = G(z) satisfies G = 1 + zG + z^2*G + z^3*G(G-1).
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EXAMPLE
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a(3)=3 because we have UDUDUD, UDUUDD, and UUDDUD.
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MAPLE
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G := ((1-z-z^2+z^3-sqrt(1-2*z-z^2-z^4-2*z^5+z^6))*1/2)/z^3: Gser := series(G, z = 0, 36): seq(coeff(Gser, z, n), n = 0 .. 31);
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CROSSREFS
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A162984
Sequence in context: A116380 A004111 A032235 this_sequence A052523 A166296 A151527
Adjacent sequences: A162982 A162983 A162984 this_sequence A162986 A162987 A162988
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 11 2009
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