A236430 Number of representations of 1 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.

2, 5, 11, 22, 42, 76, 134, 228, 379, 606, 985, 1528, 2364, 3576, 5419, 7988, 11868, 17163, 24937, 35599, 50787, 71290, 100748, 139734, 194113

Offset: 1

Author

Clark Kimberling, Jan 25 2014

Keywords

• nonn
• more

Comments

a(n) = number of partitions of 2n+1 that contain a partition of n+1.

Examples

			a(2) counts these 5 representations of 1: 3-2, 3-1-1, 2+1-2, 2+1-1-1, 1+1+1-1-1.
		

Crossrefs

Cf. A236429, A235130.

Programs

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 *)