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%I #11 Aug 04 2019 19:17:11
%S 1,0,0,2,3,0,0,3,4,0,0,15,20,0,0,23,31,0,0,55,70,0,0,153,195,0,0,265,
%T 335,0,0,535,664,0,0,988,1208,0,0,2242,2750,0,0,3580,4332,0,0,6941,
%U 8349,0,0,11621,13909,0,0,20681,24585,0,0,37202
%N Number of partitions of n such that the (sum of distinct even parts) = floor(n/2).
%e a(5) counts these 3 partitions: 32, 221, 2111.
%t Table[p = IntegerPartitions[n];
%t Length[Select[Table[Total[Select[DeleteDuplicates[p[[k]]], EvenQ]], {k, Length[p]}], # == Floor[n/2] &]], {n, 60}](* _Peter J. C. Moses_, Mar 29 2017 *)
%Y Cf. A284608, A284616, A284617.
%K nonn,easy
%O 1,4
%A _Clark Kimberling_, Mar 30 2017
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