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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, 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
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
KEYWORD
nonn,more
AUTHOR
Clark Kimberling, Sep 17 2022
EXTENSIONS
a(26) from Alois P. Heinz, Sep 17 2022
STATUS
approved