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A001860 Number of series-reduced planted trees with n+9 nodes and 4 internal nodes.
(Formerly M2917 N1171)
1
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; graph; refs; listen; history; text; internal format)
OFFSET
0,2
REFERENCES
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 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).
LINKS
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
FORMULA
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]
EXAMPLE
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........
MAPLE
A001860:=(3+3*z+2*z**2)/(z**2+z+1)/(z-1)**4; # conjectured by Simon Plouffe in his 1992 dissertation
MATHEMATICA
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 *)
PROG
(PARI) a(n)=(8*n^3+27*n^2+21*n+9)\18
CROSSREFS
Sequence in context: A124052 A215640 A104353 * A199035 A101459 A051408
KEYWORD
nonn
AUTHOR
EXTENSIONS
Additional comments from Michael Somos, Jun 06 2002
STATUS
approved

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Last modified June 22 11:42 EDT 2024. Contains 373570 sequences. (Running on oeis4.)