A308091 Sum of the areas of the integer-sided triangles with perimeter n and integer area.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 12, 0, 12, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 30, 0, 72, 0, 0, 0, 198, 0, 0, 0, 60, 0, 126, 0, 66, 0, 0, 0, 288, 0, 180, 0, 0, 0, 360, 0, 84, 0, 0, 0, 330, 0, 0, 0, 648, 0, 132, 0, 204, 0, 420, 0, 876, 0, 0, 0, 114

Offset

1,12

Links

Table of n, a(n) for n=1..76.

Wikipedia, Integer Triangle

Formula

a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} m * (1 - ceiling(m) + floor(m)) * sign(floor((i+k)/(n-i-k+1))), where m = sqrt((n/2)*(n/2-i)*(n/2-k)*(i+k-n/2)).

Mathematica

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

Crossrefs

Cf. A051516.

Sequence in context: A028615 A028704 A028607 * A096527 A028599 A270850

Adjacent sequences: A308088 A308089 A308090 * A308092 A308093 A308094

Keyword

nonn

Author

Wesley Ivan Hurt, May 12 2019

Status

approved