proposed

approved

editing

proposed

allocated for Wesley Ivan HurtSum of the even parts in the partitions of n into 9 parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 12, 18, 38, 60, 104, 152, 250, 340, 506, 688, 980, 1302, 1806, 2344, 3156, 4060, 5332, 6756, 8740, 10924, 13876, 17182, 21522, 26366, 32646, 39616, 48494, 58418, 70796, 84616, 101714, 120700, 143904, 169730, 200888, 235512

0,11

<a href="/index/Par#part">Index entries for sequences related to partitions</a>

a(n) = Sum_{q=1..floor(n/9)} Sum_{p=q..floor((n-q)/8)} Sum_{o=p..floor((n-p-q)/7)} Sum_{m=o..floor((n-o-p-q)/6)} Sum_{l=m..floor((n-m-o-p-q)/5)} Sum_{k=l..floor((n-l-m-o-p-q)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q)/2)} q * ((q-1) mod 2) + p * ((p-1) mod 2) + o * ((o-1) mod 2) + m * ((m-1) mod 2) + l * ((l-1) mod 2) + k * ((k-1) mod 2) + j * ((j-1) mod 2) + i * ((i-1) mod 2) + (n-i-j-k-l-m-o-p-q-1) * ((n-i-j-k-l-m-o-p-q-1) mod 2).

Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[i * Mod[i - 1, 2] + j * Mod[j - 1, 2] + k * Mod[k - 1, 2] + l * Mod[l - 1, 2] + m * Mod[m - 1, 2] + o * Mod[o - 1, 2] + p * Mod[p - 1, 2] + q * Mod[q - 1, 2] + (n - i - j - k - l - m - o - p - q) * Mod[n - i - j - k - l - m - o - p - q - 1, 2], {i, j, Floor[(n - j - k - l - m - o - p - q)/2]}], {j, k, Floor[(n - k - l - m - o - p - q)/3]}], {k, l, Floor[(n - l - m - o - p - q)/4]}], {l, m, Floor[(n - m - o - p - q)/5]}], {m, o, Floor[(n - o - p - q)/6]}], {o, p, Floor[(n - p - q)/7]}], {p, q, Floor[(n - q)/8]}], {q, Floor[n/9]}], {n, 0, 80}]~

allocated

nonn

Wesley Ivan Hurt, Aug 11 2019

approved

editing

allocated for Wesley Ivan Hurt

recycled

allocated

recycled

approved