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A309517
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Sum of the odd parts in the partitions of n into 4 parts.
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0
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0, 0, 0, 0, 4, 3, 8, 9, 22, 26, 50, 59, 100, 114, 168, 197, 284, 329, 438, 504, 660, 748, 946, 1072, 1322, 1488, 1794, 2008, 2408, 2671, 3130, 3465, 4024, 4434, 5100, 5595, 6384, 6966, 7866, 8565, 9630, 10449, 11648, 12600, 13992, 15080, 16652, 17912, 19684
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history;
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OFFSET
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0,5
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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)} (i * (i mod 2) + j * (j mod 2) + k * (k mod 2) + (n-i-j-k) * ((n-i-j-k) 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 ...
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a(n) | 22 26 50 59 100 ...
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MATHEMATICA
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Table[Sum[Sum[Sum[(i * Mod[i, 2] + j * Mod[j, 2] + k * Mod[k, 2] + (n - i - j - k) * Mod[n - i - j - k, 2]), {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 100}]
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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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