A309624 Sum of the odd parts in the partitions of n into 7 parts.

0, 0, 0, 0, 0, 0, 0, 7, 6, 14, 18, 37, 46, 83, 106, 179, 230, 352, 450, 667, 838, 1169, 1458, 1978, 2442, 3214, 3934, 5074, 6154, 7768, 9332, 11631, 13854, 16975, 20086, 24341, 28572, 34244, 39942, 47430, 54998, 64708, 74598, 87157, 99936, 115874, 132234

Offset

0,8

Links

Table of n, a(n) for n=0..46.

Index entries for sequences related to partitions

Formula

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

Mathematica

Table[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] + (n - i - j - k - l - m - o) * Mod[n - i - j - k - l - m - o, 2], {i, j, Floor[(n - j - k - l - m - o)/2]}], {j, k, Floor[(n - k - l - m - o)/3]}], {k, l, Floor[(n - l - m - o)/4]}], {l, m, Floor[(n - m - o)/5]}], {m, o, Floor[(n - o)/6]}], {o, Floor[n/7]}], {n, 0, 50}]

Crossrefs

Sequence in context: A297153 A363325 A259168 * A078323 A099255 A198460

Adjacent sequences: A309621 A309622 A309623 * A309625 A309626 A309627

Keyword

nonn

Author

Wesley Ivan Hurt, Aug 10 2019

Status

approved