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A001860
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Number of series-reduced planted trees with n+9 nodes and 4 internal nodes.
(Formerly M2917 N1171)
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1
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0, 3, 12, 29, 57, 99, 157, 234, 333, 456, 606, 786, 998, 1245, 1530, 1855, 2223, 2637, 3099, 3612, 4179, 4802, 5484, 6228, 7036, 7911, 8856, 9873, 10965, 12135, 13385, 14718, 16137, 17644, 19242, 20934, 22722, 24609, 26598, 28691, 30891, 33201, 35623, 38160
(list;
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listen;
history;
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OFFSET
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0,2
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REFERENCES
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Simon 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.
John Riordan, personal communication.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, Table of n, a(n) for n = 0..1000
_Simon 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.
_Simon 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
Index entries for sequences related to trees
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FORMULA
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G.f.: x*(3+3*x+2*x^2)/((1-x)^3*(1-x^3)).
[(8*n^3+27*n^2+21*n+9)/18]
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EXAMPLE
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Examples for n=1 (i=internal, e=external node):
............................................e...e
...........e.e...........e.e.e.e..........e...i..
.......e.e..i...e.........i...i.........e...i....
........i.....i.........e...i.........e...i......
...........i..............i.............i........
...........e..............e.............e........
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MAPLE
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A001860:=(3+3*z+2*z**2)/(z**2+z+1)/(z-1)**4; [Conjectured by Simon Plouffe in his 1992 dissertation.]
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MATHEMATICA
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nn = 50; CoefficientList[Series[x*(3 + 3*x + 2*x^2)/((1 - x)^3*(1 - x^3)), {x, 0, nn}], x] (* T. D. Noe, Aug 10 2012 *)
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PROG
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(PARI) a(n)=(8*n^3+27*n^2+21*n+9)\18
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CROSSREFS
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Sequence in context: A124052 A215640 A104353 * A199035 A101459 A051408
Adjacent sequences: A001857 A001858 A001859 * A001861 A001862 A001863
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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Additional comments from Michael Somos, Jun 06, 2002
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STATUS
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approved
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