OFFSET
1,10
FORMULA
a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} (1 - ceiling(i*j*(n-i-j)/n) + floor(i*j*(n-i-j)/n)).
EXAMPLE
a(9) = 1; [3,3,3];
a(10) = 2; [1,4,5], [2,3,5];
a(11) = 0;
a(12) = 3; [1,3,8], [2,4,6], [3,4,5].
MATHEMATICA
Table[Sum[Sum[(1 - Ceiling[i*j*(n - i - j)/n] + Floor[i*j*(n - i - j)/n]), {i, j, Floor[(n - j)/2]}], {j, Floor[n/3]}], {n, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Apr 09 2021
STATUS
approved