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A309547
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Sum of the even parts in the partitions of n into 5 parts.
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0
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0, 0, 0, 0, 0, 0, 2, 4, 12, 18, 38, 48, 80, 102, 164, 206, 302, 374, 522, 632, 856, 1014, 1326, 1564, 1988, 2324, 2904, 3358, 4114, 4716, 5700, 6486, 7734, 8756, 10322, 11612, 13544, 15152, 17534, 19526, 22414, 24846, 28310, 31258, 35394, 38926, 43822, 48034
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OFFSET
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0,7
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LINKS
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FORMULA
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a(n) = Sum_{l=1..floor(n/5)} Sum_{k=l..floor((n-1)/4)} Sum_{j=k..floor((n-k-l)/3)} Sum_{i=j..floor((n-j-k-l)/2)} (i * ((i-1) mod 2) + j * ((j-1) mod 2) + k * ((k-1) mod 2) + l * ((l-1) mod 2) + (n-i-j-k-l) * ((n-i-j-k-l-1) mod 2)).
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EXAMPLE
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The partitions of n into 5 parts for n = 10, 11, ..
1+1+1+1+10
1+1+1+2+9
1+1+1+3+8
1+1+1+4+7
1+1+1+5+6
1+1+1+1+9 1+1+2+2+8
1+1+1+2+8 1+1+2+3+7
1+1+1+3+7 1+1+2+4+6
1+1+1+4+6 1+1+2+5+5
1+1+1+5+5 1+1+3+3+6
1+1+1+1+8 1+1+2+2+7 1+1+3+4+5
1+1+1+2+7 1+1+2+3+6 1+1+4+4+4
1+1+1+3+6 1+1+2+4+5 1+2+2+2+7
1+1+1+1+7 1+1+1+4+5 1+1+3+3+5 1+2+2+3+6
1+1+1+2+6 1+1+2+2+6 1+1+3+4+4 1+2+2+4+5
1+1+1+3+5 1+1+2+3+5 1+2+2+2+6 1+2+3+3+5
1+1+1+1+6 1+1+1+4+4 1+1+2+4+4 1+2+2+3+5 1+2+3+4+4
1+1+1+2+5 1+1+2+2+5 1+1+3+3+4 1+2+2+4+4 1+3+3+3+4
1+1+1+3+4 1+1+2+3+4 1+2+2+2+5 1+2+3+3+4 2+2+2+2+6
1+1+2+2+4 1+1+3+3+3 1+2+2+3+4 1+3+3+3+3 2+2+2+3+5
1+1+2+3+3 1+2+2+2+4 1+2+3+3+3 2+2+2+2+5 2+2+2+4+4
1+2+2+2+3 1+2+2+3+3 2+2+2+2+4 2+2+2+3+4 2+2+3+3+4
2+2+2+2+2 2+2+2+2+3 2+2+2+3+3 2+2+3+3+3 2+3+3+3+3
--------------------------------------------------------------------------
n | 10 11 12 13 14 ...
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a(n) | 38 48 80 102 164 ...
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MATHEMATICA
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Table[Sum[Sum[Sum[Sum[i * Mod[i - 1, 2] + j * Mod[j - 1, 2] + k * Mod[k - 1, 2] + l * Mod[l - 1, 2] + (n - i - j - k - l) * Mod[n - i - j - k - l - 1, 2], {i, j, Floor[(n - j - k - l)/2]}], {j, k, Floor[(n - k - l)/3]}], {k, l, Floor[(n - l)/4]}], {l, Floor[n/5]}], {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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