OFFSET
0,7
FORMULA
a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} sign((k mod 2) + (j mod 2) + (i mod 2) + ((n-i-j-k) mod 2)).
EXAMPLE
a(7) = 3; [4,1,1,1], [3,2,1,1], [2,2,2,1].
a(8) = 4; [5,1,1,1], [4,2,1,1], [3,3,1,1], [3,2,2,1], (not [2,2,2,2]).
MATHEMATICA
Table[Sum[Sum[Sum[Sign[Mod[k, 2] + Mod[j, 2] + Mod[i, 2] + Mod[n - i - j - k, 2]], {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jan 12 2021
STATUS
approved