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%I #10 Nov 06 2018 04:21:51
%S 2,5,11,22,42,76,134,228,379,606,985,1528,2364,3576,5419,7988,11868,
%T 17163,24937,35599,50787,71290,100748,139734,194113
%N 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.
%C a(n) = number of partitions of 2n+1 that contain a partition of n+1.
%e 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.
%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. A236429, A235130.
%K nonn,more
%O 1,1
%A _Clark Kimberling_, Jan 25 2014
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