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A284619
Number of partitions of n such that the (sum of distinct even parts) >= n/2.
4
0, 1, 1, 3, 1, 3, 4, 8, 7, 13, 18, 29, 20, 33, 45, 68, 62, 92, 126, 179, 170, 240, 322, 441, 387, 530, 699, 934, 883, 1179, 1537, 2010, 1924, 2514, 3235, 4169, 4094, 5272, 6701, 8521, 7983, 10149, 12784, 16074, 15733, 19770, 24669, 30726, 29682, 36968, 45755
OFFSET
1,4
COMMENTS
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
EXAMPLE
a(4) counts these 3 partitions: 4, 22, 211.
MATHEMATICA
Table[p = IntegerPartitions[n];
Length[Select[Table[Total[Select[DeleteDuplicates[p[[k]]], EvenQ]], {k,
Length[p]}], # >= n/2 &]], {n, 54}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 02 2017
STATUS
approved