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Search: id:A114507
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| A114507 |
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Number of Dyck paths of semilength n having no ascents of length 3. |
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+0
3
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| 1, 1, 2, 4, 10, 27, 79, 240, 750, 2387, 7711, 25214, 83315, 277799, 933596, 3159187, 10755190, 36811479, 126594819, 437220744, 1515844359, 5273760446, 18406122609, 64426136558, 226108087891, 795486834627, 2804993559426
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Also number of ordered trees with n edges that have no vertices of outdegree 3.
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FORMULA
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G.f. G satisfies z^4*G^4-z^3*G^3+zG^2-G+1=0.
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EXAMPLE
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a(3)=4 because we have UDUDUD, UDUUDD, UUDDUD, and UUDUDD, where U=(1,1),
D=(1,-1).
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MAPLE
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Order:=36: Y:=solve(series((Y-Y^2)/(1-Y^3+Y^4), Y)=z, Y): seq(coeff(Y, z^n), n=1..32); #(Y=zG)
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CROSSREFS
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Cf. A102403, A114506, A114509.
Sequence in context: A002459 A104383 A108523 this_sequence A127386 A099950 A121690
Adjacent sequences: A114504 A114505 A114506 this_sequence A114508 A114509 A114510
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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), Dec 03 2005
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