cp's OEIS Frontend

A357212 a(n) = number of nonempty subsets of {1,2,...,n} having a partition into two subsets with the same sum of elements.

%I A357212 #12 Sep 18 2022 09:10:11
%S A357212 0,0,1,3,7,17,37,81,174,372,786,1650,3438,7125,14666,30048,61248,
%T A357212 124439,251921,508778,1025182,2062286,4142643,8312926,16667004,
%U A357212 33395274
%N A357212 a(n) = number of nonempty subsets of {1,2,...,n} having a partition into two subsets with the same sum of elements.
%F A357212 a(n) = Sum_{i=1..n} A232466(i).
%e A357212 The set {1,2,3,4,5,6} has 17 subsets as described, one of which is {1,2,4,5,6}, which partitions as {{1,2,6},{4,5}}
%t A357212 b[n_, i_] := b[n, i] = If[i < 1, If[n == 0, {0}, {}], If[i*(i + 1)/2 < n, {},
%t A357212     b[n, i - 1]~Union~Map[Function[p, p + x^i], b[n + i, i - 1]~Union~b[Abs[n - i], i -1]]]]; Accumulate[Table[Length[b[n, n - 1]], {n, 1, 20}]]
%t A357212 (* after Jean-François Alcover; see A232466 *)
%Y A357212 Partial sums of A232466.
%K A357212 nonn,more
%O A357212 1,4
%A A357212 _Clark Kimberling_, Sep 17 2022
%E A357212 a(26) from _Alois P. Heinz_, Sep 17 2022