A301739 The number of trees with 4 nodes labeled by positive integers, where each tree's label sum is n.

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

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

Table of n, a(n) for n=4..53.

Index entries for linear recurrences with constant coefficients, signature (1,2,-1,-2,-1,2,1,-1).

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

Adjacent sequences: A301736 A301737 A301738 * A301740 A301741 A301742

Keyword

nonn,easy

Author

R. J. Mathar, Mar 26 2018

Status

approved