cp's OEIS Frontend

A317098 Number of series-reduced rooted trees with n unlabeled leaves where the number of distinct branches under each node is <= 2.

%I A317098 #10 Aug 20 2018 20:52:32
%S A317098 1,1,2,5,12,31,80,214,576,1595,4448,12625,36146,104662,305251,897417,
%T A317098 2654072,7895394,23601441,70871693,213660535,646484951,1962507610,
%U A317098 5975425743,18243789556,55841543003,171320324878,526738779846,1622739134873,5008518981670
%N A317098 Number of series-reduced rooted trees with n unlabeled leaves where the number of distinct branches under each node is <= 2.
%C A317098 There can be more than two branches as long as there are not three distinct branches.
%H A317098 Andrew Howroyd, <a href="/A317098/b317098.txt">Table of n, a(n) for n = 1..200</a>
%e A317098 The a(5) = 12 trees:
%e A317098   (o(o(o(oo))))
%e A317098   (o(o(ooo)))
%e A317098   (o((oo)(oo)))
%e A317098   (o(oo(oo)))
%e A317098   (o(oooo))
%e A317098   ((oo)(o(oo)))
%e A317098   ((oo)(ooo))
%e A317098   (oo(o(oo)))
%e A317098   (oo(ooo))
%e A317098   (o(oo)(oo))
%e A317098   (ooo(oo))
%e A317098   (ooooo)
%t A317098 semisameQ[u_]:=Length[Union[u]]<=2;
%t A317098 nms[n_]:=nms[n]=If[n==1,{{1}},Join@@Table[Select[Union[Sort/@Tuples[nms/@ptn]],semisameQ],{ptn,Rest[IntegerPartitions[n]]}]];
%t A317098 Table[Length[nms[n]],{n,10}]
%o A317098 (PARI) seq(n)={my(v=vector(n)); v[1]=1; for(n=2, n, v[n]=sum(k=1, n-1, sumdiv(k, d, v[d])*sumdiv(n-k, d, v[d])/2) + sumdiv(n, d, v[n/d]*(1 - (d-1)/2)) ); v} \\ _Andrew Howroyd_, Aug 19 2018
%Y A317098 Cf. A000081, A000598, A001190, A055277, A111299, A292050, A298204, A301344, A317097.
%K A317098 nonn
%O A317098 1,3
%A A317098 _Gus Wiseman_, Aug 01 2018
%E A317098 Terms a(21) and beyond from _Andrew Howroyd_, Aug 19 2018