login
A308302
Number of integer-sided triangles with perimeter n and at least one nonsquare side length.
0
0, 0, 0, 0, 1, 1, 2, 1, 2, 2, 4, 2, 5, 4, 7, 5, 8, 7, 9, 8, 12, 9, 14, 12, 16, 14, 18, 16, 21, 19, 24, 21, 26, 23, 30, 26, 33, 30, 37, 33, 39, 37, 44, 40, 48, 44, 52, 47, 56, 52, 60, 56, 65, 60, 70, 65, 74, 70, 79, 75, 85, 80, 91, 85, 96, 90, 102, 96, 108
OFFSET
1,7
FORMULA
a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} sign(floor((i+k)/(n-i-k+1))) * (1 - A010052(i) * A010052(k) * A010052(n-i-k)).
a(n) = A005044(n) - A308064(n).
MATHEMATICA
Table[Sum[Sum[(1 - (Floor[Sqrt[i]] - Floor[Sqrt[i - 1]]) (Floor[Sqrt[k]] - Floor[Sqrt[k - 1]]) (Floor[Sqrt[n - k - i]] - Floor[Sqrt[n - k - i - 1]]))*Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, May 19 2019
STATUS
approved