cp's OEIS Frontend

A317099 Number of series-reduced planted achiral trees whose leaves span an initial interval of positive integers appearing with multiplicities an integer partition of n.

%I A317099 #9 Aug 01 2018 20:37:28
%S A317099 1,3,4,9,8,19,16,35,35,54,57,113,102,155,189,279,298,447,491,702,813,
%T A317099 1063,1256,1759,1967,2542,3050,3902,4566,5882,6843,8676,10205,12612,
%U A317099 14908,18608,21638,26510,31292,38150,44584,54185,63262,76308,89371,106818,124755
%N A317099 Number of series-reduced planted achiral trees whose leaves span an initial interval of positive integers appearing with multiplicities an integer partition of n.
%C A317099 In these trees, achiral means that all branches directly under any given node that is not a leaf or a cover of leaves are equal, and series-reduced means that every node that is not a leaf or a cover of leaves has at least two branches.
%e A317099 The a(4) = 9 trees:
%e A317099   (1111), ((11)(11)), (((1)(1))((1)(1))), ((1)(1)(1)(1)),
%e A317099   (1112),
%e A317099   (1122), ((12)(12)),
%e A317099   (1123),
%e A317099   (1234).
%e A317099 The a(6) = 19 trees:
%e A317099   (111111), ((111)(111)), (((1)(1)(1))((1)(1)(1))), ((11)(11)(11)), (((1)(1))((1)(1))((1)(1))), ((1)(1)(1)(1)(1)(1)),
%e A317099   (111112),
%e A317099   (111122), ((112)(112)),
%e A317099   (111123),
%e A317099   (111222), ((12)(12)(12)),
%e A317099   (111223),
%e A317099   (111234),
%e A317099   (112233), ((123)(123)),
%e A317099   (112234),
%e A317099   (112345),
%e A317099   (123456).
%t A317099 b[n_]:=1+Sum[b[n/d],{d,Rest[Divisors[n]]}];
%t A317099 a[n_]:=Sum[b[GCD@@Length/@Split[ptn]],{ptn,IntegerPartitions[n]}];
%t A317099 Array[a,30]
%Y A317099 Cf. A001678, A003238, A052409, A052410, A067824, A167865, A168532, A214577, A289078, A294336, A316782, A317100.
%K A317099 nonn
%O A317099 1,2
%A A317099 _Gus Wiseman_, Aug 01 2018