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
Examples
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.
Programs
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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 *)
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