A236429 Number of representations of 0 as a sum of numbers d*k with d in {-1,1} and k in {1,2,...,n}, where the sum of the numbers k is 2n.

1, 3, 6, 14, 25, 52, 86, 160, 260, 443, 688, 1146, 1721, 2716, 4040, 6176, 8975, 13482, 19218, 28167, 39799, 57081, 79503, 112987, 155368

Offset

1,2

Comments

a(n) = number of partitions of 2n that contain a partition of n.

Links

Table of n, a(n) for n=1..25.

Example

a(3) counts these 6 representations of 0: 3-3, 3-2-1, 3-1-1-1, 2+1-2-1, 2+1-1-1-1, 1+1+1-1-1-1.

Mathematica

p[n_] := p[n] = IntegerPartitions[n]; Map[({p1 = p[#], p2 = p[2 #]} &[#];    Length[Cases[p2, Apply[Alternatives, Map[Flatten[{___, #, ___}] &, p1]]]]) &,  Range[12]]
Map[({p1 = p[# + 1], p2 = p[2 # + 1]} &[#]; Length[Cases[p2, Apply[Alternatives, Map[Flatten[{___, #, ___}] &, p1]]]]) &, Range[12]]
(* Peter J. C. Moses, Jan 04 2014 *)

Crossrefs

Cf. A236430, A235130.

Sequence in context: A166212 A291988 A285460 * A316245 A002219 A006906

Adjacent sequences: A236426 A236427 A236428 * A236430 A236431 A236432

Keyword

nonn,more

Author

Clark Kimberling, Jan 25 2014

Status

approved