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A014301
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Number of internal nodes of even outdegree in all ordered rooted trees with n edges.
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15
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0, 1, 3, 11, 40, 148, 553, 2083, 7896, 30086, 115126, 442118, 1703052, 6577474, 25461493, 98759971, 383751472, 1493506534, 5820778858, 22714926826, 88745372992, 347087585824, 1358789148058, 5324148664846
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Number of protected vertices in all ordered rooted trees with n edges. A protected vertex in an ordered tree is a vertex at least 2 edges away from its leaf descendants. [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 20 2008]
1,3,11,... gives the diagonal sums of A111418. Hankel transform of a(n) is A128834. Hankel transform of a(n+1) is A187340. [Paul Barry, Mar 8 2011]
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REFERENCES
| Gi-Sang Cheon and Louis W. Shapiro, Protected points in ordered trees, Appl. Math. Letters, 21, 2008, 516-520. [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 20 2008]
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LINKS
| Torleiv Klove, Spheres of Permutations under the Infinity Norm - Permutations with limited displacement. Reports in Informatics, Department of Informatics, University of Bergen, Norway, no. 376, November 2008.
Index entries for sequences related to rooted trees
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FORMULA
| Binomial(2*n-1, n)/3 - A000957(n)/3;
(1/2)*Sum_{k=0..n} (-1)^(n-k)*binomial(n+k-1, k). - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 28 2002
G.f.: [1-2z-sqrt(1-4z)]/[3sqrt(1-4z)-1+4z]. a(n)=[A026641(n)-A026641(n-1)]/3 for n>1. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 26 2004
a(n)=(1/2)sum(binomial(2n-2j-2, n-2), j=0..floor(n/2)).
a(n)=sum{k=0..n, (-1)^(n-k)*C(n+k,k-1)}; - Paul Barry (pbarry(AT)wit.ie), Jul 18 2006
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CROSSREFS
| Cf. A059481.
Cf. A026641.
A143362, A143363 [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 20 2008]
Sequence in context: A010911 A108153 A052941 * A119375 A149063 A149064
Adjacent sequences: A014298 A014299 A014300 * A014302 A014303 A014304
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu)
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