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A309800
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Sum of the even parts appearing among the largest parts of the partitions of n into 4 parts.
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0
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0, 0, 0, 0, 0, 2, 2, 6, 6, 14, 18, 32, 38, 62, 72, 104, 122, 170, 200, 264, 302, 388, 444, 554, 628, 768, 866, 1036, 1160, 1376, 1532, 1788, 1976, 2280, 2518, 2880, 3160, 3590, 3920, 4410, 4802, 5374, 5838, 6492, 7018, 7766, 8378, 9224, 9922, 10878, 11674
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OFFSET
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0,6
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LINKS
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FORMULA
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a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} (n-i-j-k) * ((n-i-j-k-1) mod 2).
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EXAMPLE
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Figure 1: The partitions of n into 4 parts for n = 8, 9, ..
1+1+1+9
1+1+2+8
1+1+3+7
1+1+4+6
1+1+1+8 1+1+5+5
1+1+2+7 1+2+2+7
1+1+1+7 1+1+3+6 1+2+3+6
1+1+2+6 1+1+4+5 1+2+4+5
1+1+3+5 1+2+2+6 1+3+3+5
1+1+1+6 1+1+4+4 1+2+3+5 1+3+4+4
1+1+1+5 1+1+2+5 1+2+2+5 1+2+4+4 2+2+2+6
1+1+2+4 1+1+3+4 1+2+3+4 1+3+3+4 2+2+3+5
1+1+3+3 1+2+2+4 1+3+3+3 2+2+2+5 2+2+4+4
1+2+2+3 1+2+3+3 2+2+2+4 2+2+3+4 2+3+3+4
2+2+2+2 2+2+2+3 2+2+3+3 2+3+3+3 3+3+3+3
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n | 8 9 10 11 12 ...
--------------------------------------------------------------------------
a(n) | 6 14 18 32 38 ...
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MATHEMATICA
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Table[Sum[Sum[Sum[(n - i - j - k)*Mod[n - i - j - k - 1, 2], {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 50}]
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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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