A308303 Number of integer-sided triangles with perimeter n and at least one even side length.

0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 4, 5, 6, 7, 6, 8, 9, 10, 9, 12, 12, 14, 12, 16, 16, 19, 16, 21, 20, 24, 20, 27, 25, 30, 25, 33, 30, 37, 30, 40, 36, 44, 36, 48, 42, 52, 42, 56, 49, 61, 49, 65, 56, 70, 56, 75, 64, 80, 64, 85, 72, 91, 72, 96, 81, 102

Offset: 1

Author

Wesley Ivan Hurt, May 19 2019

Keywords

• nonn

Links

• Wikipedia, Integer Triangle

Crossrefs

Cf. A005044, A308065.

Programs

Mathematica

Table[Sum[Sum[(1 - Mod[i, 2] Mod[k, 2] Mod[n - i - k, 2])*Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]

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 - (i mod 2) * (k mod 2) * ((n-i-k) mod 2)).

a(n) = A005044(n) - A308065(n).