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

Author

R. J. Mathar, Mar 26 2018

Keywords

• nonn
• easy

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.

Examples

			a(4)=2 because there is a linear tree with all labels equal 1 and the star tree with all labels equal to 1.
		

Links

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

Crossrefs

4th column of A303841.

Programs

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](%) ;

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) ).