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%I #10 Aug 14 2023 08:11:50
%S 0,1,1,3,1,3,4,8,7,13,18,29,20,33,45,68,62,92,126,179,170,240,322,441,
%T 387,530,699,934,883,1179,1537,2010,1924,2514,3235,4169,4094,5272,
%U 6701,8521,7983,10149,12784,16074,15733,19770,24669,30726,29682,36968,45755
%N Number of partitions of n such that the (sum of distinct even parts) >= n/2.
%C The number of partitions of n such that (sum distinct even parts) = n/2 is A284617(n)-A284616(n) = A284619(n)-A284618(n) = 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 15, 0, 0, 0, 23, 0, 0, 0, 55, 0, 0, 0, 153, 0, 0, 0, 265,... (offset 1, nonzero for 4|n) - _R. J. Mathar_, Aug 14 2023
%e a(4) counts these 3 partitions: 4, 22, 211.
%t Table[p = IntegerPartitions[n];
%t Length[Select[Table[Total[Select[DeleteDuplicates[p[[k]]], EvenQ]], {k,
%t Length[p]}], # >= n/2 &]], {n, 54}]
%Y Cf. A284616, A284617, A284618.
%K nonn,easy
%O 1,4
%A _Clark Kimberling_, Apr 02 2017