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Search: id:A114509
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| A114509 |
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Number of Dyck paths of semilength n having no ascents of length 4. |
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+0
3
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| 1, 1, 2, 5, 13, 37, 111, 345, 1104, 3611, 12016, 40548, 138414, 477076, 1657956, 5802920, 20436910, 72369903, 257518806, 920333307, 3302003826, 11888979066, 42944410207, 155576009845, 565127618392, 2057903975752, 7510967300206
(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 4.
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FORMULA
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G.f. G=G(z) satisfies z^5*G^5-z^4*G^4+zG^2-G+1=0.
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EXAMPLE
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a(4)=13 because among the Catalan(4)=14 Dyck paths of semilength 4 only UUUUDDDD has an ascent of length 4 (here U=(1,1), D=(1,-1)).
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MAPLE
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Order:=35: Y:=solve(series((Y-Y^2)/(1-Y^4+Y^5), Y)=z, Y): seq(coeff(Y, z^n), n=1..30); #(Y=zG)
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CROSSREFS
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Cf. A102403, A114507, A114508.
Sequence in context: A005961 A036249 A126031 this_sequence A003080 A053732 A119495
Adjacent sequences: A114506 A114507 A114508 this_sequence A114510 A114511 A114512
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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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