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A301739 The number of trees with 4 nodes labeled by positive integers, where each tree's label sum is n. 2
2, 4, 10, 17, 30, 44, 67, 91, 126, 163, 213, 265, 333, 403, 491, 582, 693, 807, 944, 1084, 1249, 1418, 1614, 1814, 2044, 2278, 2544, 2815, 3120, 3430, 3777, 4129, 4520, 4917, 5355, 5799, 6287, 6781, 7321, 7868, 8463, 9065, 9718, 10378, 11091, 11812, 12588, 13372, 14214, 15064 (list; graph; refs; listen; history; text; internal format)
OFFSET
4,1
COMMENTS
Computed by the sum over the A000055(4)=2 shapes of the trees: the linear graph of the n-Butane, and the star graph of (1)-Methyl-Propane.
LINKS
FORMULA
a(n) = A005993(n-4)+A000601(n-4).
G.f.: x^4*(2+2*x+2*x^2+x^3+x^4)/((1+x)^2*(x-1)^4*(1+x+x^2) ).
EXAMPLE
a(4)=2 because there is a linear tree with all labels equal 1 and the star tree with all labels equal to 1.
MAPLE
x^4*(2+2*x+2*x^2+x^3+x^4)/(1+x)^2/(x-1)^4/(1+x+x^2) ;
taylor(%, x=0, 80) ;
gfun[seriestolist](%) ;
CROSSREFS
4th column of A303841.
Sequence in context: A125754 A097870 A244474 * A152231 A285939 A034455
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Mar 26 2018
STATUS
approved

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Last modified July 21 05:28 EDT 2024. Contains 374463 sequences. (Running on oeis4.)