|
%I #11 Nov 06 2018 04:21:22
%S 1,3,6,14,25,52,86,160,260,443,688,1146,1721,2716,4040,6176,8975,
%T 13482,19218,28167,39799,57081,79503,112987,155368
%N 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.
%C a(n) = number of partitions of 2n that contain a partition of n.
%e 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.
%t p[n_] := p[n] = IntegerPartitions[n]; Map[({p1 = p[#], p2 = p[2 #]} &[#]; Length[Cases[p2, Apply[Alternatives, Map[Flatten[{___, #, ___}] &, p1]]]]) &, Range[12]]
%t Map[({p1 = p[# + 1], p2 = p[2 # + 1]} &[#]; Length[Cases[p2, Apply[Alternatives, Map[Flatten[{___, #, ___}] &, p1]]]]) &, Range[12]]
%t (* _Peter J. C. Moses_, Jan 04 2014 *)
%Y Cf. A236430, A235130.
%K nonn,more
%O 1,2
%A _Clark Kimberling_, Jan 25 2014
|
