cp's OEIS Frontend

A318228 Number of inequivalent leaf-colorings of planted achiral trees with n nodes.

%I A318228 #10 Dec 14 2020 01:37:22
%S A318228 1,1,3,6,13,20,43,58,115,171,323,379,1034,1135,2321,4327,8915,9212,
%T A318228 33939,34429,128414,234017,417721,418976,2931624,5096391,11770830,
%U A318228 20357876,64853630,64858195
%N A318228 Number of inequivalent leaf-colorings of planted achiral trees with n nodes.
%C A318228 In a planted achiral tree, all branches directly under any given branch are identical.
%e A318228 Inequivalent representatives of the a(5) = 13 leaf-colorings:
%e A318228   (1111)  ((111))  ((1)(1))  (((11)))  ((((1))))
%e A318228   (1112)  ((112))  ((1)(2))  (((12)))
%e A318228   (1122)  ((123))
%e A318228   (1123)
%e A318228   (1234)
%o A318228 (PARI) \\ See links in A339645 for combinatorial species functions.
%o A318228 G(v)={my(t=2, p=sv(1)); for(i=1, #v, my(d=v[i]); if(d>1, p=sApplyCI(symGroupCycleIndex(d), d, p, t)); t=t*d+1); p}
%o A318228 cycleIndex(n)={my(recurse(r,v)=if(r==1, G(v), sumdiv(r-1, d, self()((r-1)/d, concat(d,v))))); recurse(n,[])}
%o A318228 a(n)={StructsByCycleIndex(n, cycleIndex(n), n)} \\ _Andrew Howroyd_, Dec 13 2020
%Y A318228 Cf. A000081, A001190, A001678, A003238, A004111, A214577, A290689, A304486.
%Y A318228 Cf. A318226, A318227, A318229, A318230, A318231, A318234, A339645.
%K A318228 nonn,more
%O A318228 1,3
%A A318228 _Gus Wiseman_, Aug 21 2018
%E A318228 a(9)-a(30) from _Andrew Howroyd_, Dec 11 2020