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Search: id:A003120
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| A003120 |
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Number of arborescences of type (n,1), or tapeworms.
(Formerly M0836)
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+0
1
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| 1, 1, 2, 3, 7, 13, 31, 66, 159, 363, 876, 2065, 4985, 11915, 28765, 69156, 166957, 402373, 971414, 2343519, 5657755, 13654969, 32966011, 79577190, 192116331, 463786191, 1119678912, 2703086893, 6525829037, 15754607063, 38034986041
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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The g.f. -(z-1)*(3*z**2+z-1)/(-1+3*z+z**2-7*z**3+3*z**4) conjectured by S. Plouffe in his 1992 dissertation is wrong.
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REFERENCES
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J.-C. Arditti, Denombrement des arborescences dont le graphe de comparabilite est Hamiltonien, Discrete Math., 5 (1973), 189-200.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Gy. Tasi and F. Mizukami, Quantum algebraic-combinatoric study of the conformational properties of n-alkanes, J. Math. Chemistry, 25, 1999, 55-64 (see p. 63).
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LINKS
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S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Index entries for sequences related to rooted trees
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FORMULA
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G.f.:(-1-x^5-3*x^3+2*x^2+2*x)/((x-1)*(x^2+2*x-1)*(x^4+2*x^2-1)) [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009]
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MAPLE
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A003120 := n->if n mod 2 = 0 then (1/4)*(A001333(n-2)+A001333((n-2)/2)+A001333((n-4)/2)+1) else (1/4)*(A001333(n-2)+A001333((n-1)/2)+A001333((n-3)/2)+1); fi;
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CROSSREFS
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Sequence in context: A014234 A124430 A002013 this_sequence A032131 A007827 A129859
Adjacent sequences: A003117 A003118 A003119 this_sequence A003121 A003122 A003123
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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