OFFSET
1,8
FORMULA
a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} sign(c(i/j) + c((n-i-j)/i) + c((n-i-j)/j)) * (1 - [j = i]) * (1 - [n-j = 2*i]), where c(n) = ceiling(n) - floor(n) and [ ] is the Iverson bracket.
EXAMPLE
a(9) = 2; [1,3,5], [2,3,4] (Not counted: [1,1,7], [1,2,6], [1,4,4], [2,2,5], [3,3,3]).
MATHEMATICA
Table[Sum[Sum[(1 - KroneckerDelta[i, j]) (1 - KroneckerDelta[2 i, n - j]) Sign[(Ceiling[i/j] - Floor[i/j]) + (Ceiling[(n - i - j)/j] - Floor[(n - i - j)/j]) + (Ceiling[(n - i - j)/i] - Floor[(n - i - j)/i])], {i, j, Floor[(n - j)/2]}], {j, Floor[n/3]}], {n, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Apr 13 2021
STATUS
approved