OFFSET
0,9
FORMULA
a(n) = Sum_{m=1..floor(n/6)} Sum_{l=m..floor((n-m)/5)} Sum_{k=l..floor((n-l-m)/4)} Sum_{j=k..floor((n-k-l-m)/3)} Sum_(i=j..floor((n-j-k-l-m)/2)} (((i-1) mod 2) + ((j-1) mod 2) + ((k-1) mod 2) + ((l-1) mod 2) + ((m-1) mod 2) + ((n-i-j-k-l-m-1) mod 2)).
MATHEMATICA
Table[Sum[Sum[Sum[Sum[Sum[ Mod[i - 1, 2] + Mod[j - 1, 2] + Mod[k - 1, 2] + Mod[l - 1, 2] + Mod[m - 1, 2] + Mod[n - i - j - k - l - m - 1, 2], {i, j, Floor[(n - j - k - l - m)/2]}], {j, k, Floor[(n - k - l - m)/3]}], {k, l, Floor[(n - l - m)/4]}], {l, m, Floor[(n - m)/5]}], {m, Floor[n/6]}], {n, 0, 50}]
Table[Count[Flatten[IntegerPartitions[n, {6}]], _?EvenQ], {n, 0, 50}] (* Harvey P. Dale, Oct 04 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Aug 07 2019
STATUS
approved