OFFSET
0,8
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 mod 2) + (m mod 2) + (l mod 2) + (k mod 2) + (j mod 2) + (i mod 2) + ((n-i-j-k-l-m-o) mod 2).
MATHEMATICA
Table[Sum[Sum[Sum[Sum[Sum[Sum[Mod[i, 2] + Mod[j, 2] + Mod[k, 2] + Mod[l, 2] + Mod[m, 2] + Mod[o, 2] + 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}]
Table[Count[Flatten[IntegerPartitions[n, {7}]], _?OddQ], {n, 0, 50}] (* Harvey P. Dale, Feb 28 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Aug 10 2019
STATUS
approved