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A309661
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Sum of the odd parts in the partitions of n into 10 parts.
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0
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 9, 20, 27, 52, 67, 116, 151, 244, 320, 480, 631, 924, 1199, 1676, 2172, 2966, 3791, 5054, 6405, 8374, 10501, 13472, 16762, 21244, 26183, 32714, 40034, 49500, 60081, 73554, 88664, 107582, 128818, 155000, 184456, 220400
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OFFSET
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0,11
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LINKS
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FORMULA
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a(n) = Sum_{r=1..floor(n/10)} Sum_{q=r..floor((n-r)/9)} Sum_{p=q..floor((n-q-r)/8)} Sum_{o=p..floor((n-p-q-r)/7)} Sum_{m=o..floor((n-o-p-q-r)/6)} Sum_{l=m..floor((n-m-o-p-q-r)/5)} Sum_{k=l..floor((n-l-m-o-p-q-r)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q-r)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q-r)/2)} r * (r mod 2) + q * (q mod 2) + p * (p mod 2) + o * (o mod 2) + m * (m mod 2) + l * (l mod 2) + k * (k mod 2) + j * (j mod 2) + i * (i mod 2) + (n-i-j-k-l-m-o-p-q-r) * ((n-i-j-k-l-m-o-p-q-r) mod 2).
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MATHEMATICA
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Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[i * Mod[i, 2] + j * Mod[j, 2] + k * Mod[k, 2] + l * Mod[l, 2] + m * Mod[m, 2] + o * Mod[o, 2] + p * Mod[p, 2] + q * Mod[q, 2] + r * Mod[r, 2] + (n - i - j - k - l - m - o - p - q - r) * Mod[n - i - j - k - l - m - o - p - q - r, 2], {i, j, Floor[(n - j - k - l - m - o - p - q - r)/2]}], {j, k, Floor[(n - k - l - m - o - p - q - r)/3]}], {k, l, Floor[(n - l - m - o - p - q - r)/4]}], {l, m, Floor[(n - m - o - p - q - r)/5]}], {m, o, Floor[(n - o - p - q - r)/6]}], {o, p, Floor[(n - p - q - r)/7]}], {p, q, Floor[(n - q - r)/8]}], {q, r, Floor[(n - r)/9]}], {r, Floor[n/10]}], {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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