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Number of partitions of n such that the (sum of distinct odd parts) <= n/2.
4

%I #4 Apr 02 2017 09:46:17

%S 0,2,2,4,4,8,9,18,22,32,40,61,75,99,126,176,215,300,375,491,602,786,

%T 971,1235,1491,1936,2359,2917,3499,4423,5326,6684,7956,9917,11833,

%U 14511,17155,20987,24845,30387,35688,43221,50803,61535,71893,85909,100369,120887

%N Number of partitions of n such that the (sum of distinct odd parts) <= n/2.

%e a(4) counts these 4 partitions: 4, 31, 211, 1111.

%t Table[p = IntegerPartitions[n];

%t Length[Select[Table[Total[Select[DeleteDuplicates[p[[k]]], OddQ]], {k, Length[p]}], # <= n/2 &]], {n, 55}]

%Y Cf. A284612, A284614, A284615.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Mar 30 2017