cp's OEIS Frontend

A317097 Number of rooted trees with n nodes where the number of distinct branches under each node is <= 2.

%I A317097 #12 Aug 28 2018 19:55:19
%S A317097 1,1,2,4,9,20,46,106,248,583,1393,3343,8111,19801,48719,120489,299787,
%T A317097 749258,1881216,4741340,11993672,30436507,77471471,197726053,
%U A317097 505917729,1297471092,3334630086,8587369072,22155278381,57259037225,148222036272,384272253397
%N A317097 Number of rooted trees with n nodes where the number of distinct branches under each node is <= 2.
%C A317097 There can be more than two branches as long as there are not three distinct branches.
%H A317097 Andrew Howroyd, <a href="/A317097/b317097.txt">Table of n, a(n) for n = 1..200</a>
%e A317097 The a(5) = 9 trees:
%e A317097   ((((o))))
%e A317097   (((oo)))
%e A317097   ((o(o)))
%e A317097   ((ooo))
%e A317097   (o((o)))
%e A317097   (o(oo))
%e A317097   ((o)(o))
%e A317097   (oo(o))
%e A317097   (oooo)
%t A317097 semisameQ[u_]:=Length[Union[u]]<=2;
%t A317097 nms[n_]:=nms[n]=If[n==1,{{}},Join@@Table[Select[Union[Sort/@Tuples[nms/@ptn]],semisameQ],{ptn,IntegerPartitions[n-1]}]];
%t A317097 Table[Length[nms[n]],{n,10}]
%o A317097 (PARI) seq(n)={my(v=vector(n)); v[1]=1; for(n=1, n-1, v[n+1]=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 28 2018
%Y A317097 Cf. A000081, A000598, A001190, A003238, A055277, A111299, A292050, A298204, A301344, A317098.
%K A317097 nonn
%O A317097 1,3
%A A317097 _Gus Wiseman_, Aug 01 2018
%E A317097 Terms a(20) and beyond from _Andrew Howroyd_, Aug 28 2018