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Search: id:A047891
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| A047891 |
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Number of planar rooted trees with n nodes and tricolored end nodes. |
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+0 15
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| 1, 3, 12, 57, 300, 1686, 9912, 60213, 374988, 2381322, 15361896, 100389306, 663180024, 4421490924, 29712558576, 201046204173, 1368578002188, 9366084668802, 64403308499592, 444739795023054, 3082969991029800
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Also number of lattice paths from (0,0) to (n,n), with steps (1,0),(0,1), and (1,1), that never rise above the line y=x and the steps (1,1) are colored red or blue. - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 28 2003
The Hankel transform (see A001906 for definition) of this sequence forms A049656(n+1)= [1, 3, 27, 729, 59049, 14348907, ... ] . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 29 2006
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REFERENCES
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Paul Barry, On Integer-Sequence-Based Constructions of Generalized Pascal Triangles, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.4.
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LINKS
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Index entries for sequences related to rooted trees
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FORMULA
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(1-2z-sqrt(4z^2-8z+1))/2z.
For n>0, a(n)=(1/n)*sum(k=0, n, 3^k*C(n, k)*C(n, k-1)) - Benoit Cloitre (benoit7848c(AT)orange.fr), May 10 2003
a(1)=1, a(n)=2*a(n-1)+sum(i=1, n-1, a(i)*a(n-i)). - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 16 2004
The Hankel transform (see A001906 for definition) of this sequence form A049656(n+1)= [1, 3, 27, 729, 59049, 14348907, ... ] . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 29 2006
2*a(n)=A054872(n+1). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 17 2007
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PROGRAM
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(PARI) a(n)=if(n<1, 1, sum(k=0, n, 3^k*binomial(n, k)*binomial(n, k-1))/n)
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CROSSREFS
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Essentially the same as A025231.
Cf. A006318.
Adjacent sequences: A047888 A047889 A047890 this_sequence A047892 A047893 A047894
Sequence in context: A110309 A101106 A133158 this_sequence A103370 A094149 A117107
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KEYWORD
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nonn,eigen,easy
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AUTHOR
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Louis Shapiro (lshapiro(AT)howard.edu)
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EXTENSIONS
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More terms from Christian Bower, Dec 11 1999
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