A284615 - OEIS

%I #4 Apr 03 2017 20:31:48

%S 1,1,1,1,3,4,6,9,8,11,16,24,26,37,50,75,82,113,115,166,190,259,284,

%T 400,467,619,651,887,1066,1394,1516,2020,2187,2809,3050,3983,4482,

%U 5691,6340,8149,8895,11158,12458,15796,17241,21452,24385,30582,33078,40775

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

%F a(5) counts these 3 partitions: 5, 32, 311.

%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, A284613, A284614.

%K nonn,easy

%O 1,5

%A _Clark Kimberling_, Apr 02 2017