cp's OEIS Frontend

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

%I A301739 #11 May 02 2018 06:12:16
%S A301739 2,4,10,17,30,44,67,91,126,163,213,265,333,403,491,582,693,807,944,
%T A301739 1084,1249,1418,1614,1814,2044,2278,2544,2815,3120,3430,3777,4129,
%U A301739 4520,4917,5355,5799,6287,6781,7321,7868,8463,9065,9718,10378,11091,11812,12588,13372,14214,15064
%N A301739 The number of trees with 4 nodes labeled by positive integers, where each tree's label sum is n.
%C A301739 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.
%H A301739 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-1,-2,-1,2,1,-1).
%F A301739 a(n) = A005993(n-4)+A000601(n-4).
%F A301739 G.f.: x^4*(2+2*x+2*x^2+x^3+x^4)/((1+x)^2*(x-1)^4*(1+x+x^2) ).
%e A301739 a(4)=2 because there is a linear tree with all labels equal 1 and the star tree with all labels equal to 1.
%p A301739 x^4*(2+2*x+2*x^2+x^3+x^4)/(1+x)^2/(x-1)^4/(1+x+x^2) ;
%p A301739 taylor(%,x=0,80) ;
%p A301739 gfun[seriestolist](%) ;
%Y A301739 4th column of A303841.
%K A301739 nonn,easy
%O A301739 4,1
%A A301739 _R. J. Mathar_, Mar 26 2018