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A284611
Number of partitions of n such that the (sum of all even parts) = floor(n/2).
1
1, 0, 0, 1, 2, 0, 0, 4, 6, 0, 0, 12, 15, 0, 0, 30, 40, 0, 0, 70, 84, 0, 0, 165, 198, 0, 0, 330, 405, 0, 0, 704, 836, 0, 0, 1380, 1620, 0, 0, 2688, 3192, 0, 0, 4984, 5824, 0, 0, 9394, 10934, 0, 0, 16665, 19392, 0, 0, 29970, 34560, 0, 0, 52096
OFFSET
1,5
EXAMPLE
a(8) counts these 3 partitions: 44, 431, 4111.
MATHEMATICA
Table[p = IntegerPartitions[n];
Length[Select[Table[Total[Select[p[[k]], EvenQ]], {k, Length[p]}], # ==
Floor[n/2] &]], {n, 60}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Mar 30 2017
STATUS
approved