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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 T. D. Noe, Table of n, a(n) for n = 0..1000 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 Index entries for sequences related to rooted trees Index entries for sequences related to trees Index entries for linear recurrences with constant coefficients, signature (3, -3, 2, -3, 3, -1). 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 Adjacent sequences: A001857 A001858 A001859 * A001861 A001862 A001863 KEYWORD nonn AUTHOR N. J. A. Sloane 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.)