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

1,4

Links

Table of n, a(n) for n=1..26.

Formula

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

Example

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}}

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 *)

Crossrefs

Partial sums of A232466.

Sequence in context: A026668 A111210 A033489 * A323583 A336724 A178941

Adjacent sequences: A357209 A357210 A357211 * A357213 A357214 A357215

Keyword

nonn,more

Author

Clark Kimberling, Sep 17 2022

Extensions

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

Status

approved