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A309625
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Number of even parts in the partitions of n into 7 parts.
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0
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0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 5, 8, 15, 24, 39, 50, 74, 98, 135, 174, 232, 292, 381, 470, 595, 728, 904, 1086, 1330, 1582, 1906, 2246, 2676, 3126, 3687, 4272, 4989, 5746, 6657, 7610, 8754, 9954, 11373, 12862, 14608, 16440, 18573, 20806, 23384, 26094, 29194
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OFFSET
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0,10
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LINKS
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FORMULA
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a(n) = Sum_{o=1..floor(n/7)} Sum_{m=o..floor((n-o)/6)} Sum_{l=m..floor((n-m-o)/5)} Sum_{k=l..floor((n-l-m-o)/4)} Sum_{j=k..floor((n-k-l-m-o)/3} Sum_{i=j..floor((n-j-k-l-m-o)/2)} ((o-1) mod 2) + ((m-1) mod 2) + ((l-1) mod 2) + ((k-1) mod 2) + ((j-1) mod 2) + ((i-1) mod 2) + ((n-i-j-k-l-m-o-1) mod 2).
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MATHEMATICA
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Table[Count[Flatten[IntegerPartitions[n, {7}]], _?EvenQ], {n, 0, 50}] (* Harvey P. Dale, Dec 18 2021 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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