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

0, 0, 1, 3, 7, 17, 37, 81, 174, 372, 786, 1650, 3438, 7125, 14666, 30048, 61248, 124439, 251921, 508778, 1025182, 2062286, 4142643, 8312926, 16667004, 33395274

Offset: 1

Author

Clark Kimberling, Sep 17 2022

Keywords

• nonn
• more

Examples

			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}}
		

Crossrefs

Partial sums of A232466.

Programs

Mathematica

b[n_, i_] := b[n, i] = If[i < 1, If[n == 0, {0}, {}], If[i*(i + 1)/2 < n, {},
    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}]]
(* after Jean-François Alcover; see A232466 *)

Formula

a(n) = Sum_{i=1..n} A232466(i).

Extensions

a(26) from Alois P. Heinz, Sep 17 2022