A308097 Take the integer-sided triangles with perimeter n and integer area. Then a(n) is the sum of the areas of all the triangles and the squares on their sides.
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, 98, 0, 126, 0, 0, 0, 0, 0, 224, 0, 0, 0, 0, 0, 368, 0, 826, 0, 0, 0, 2012, 0, 0, 0, 638, 0, 1390, 0, 756, 0, 0, 0, 2692, 0, 1928, 0, 0, 0, 4764, 0, 1334, 0, 0, 0, 4434, 0, 0, 0, 8354, 0, 1778, 0, 1794, 0, 3800, 0
Offset: 1
Keywords
Links
- Wikipedia, Integer Triangle
Crossrefs
Cf. A308091.
Programs
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Mathematica
Table[Sum[Sum[(i^2 + k^2 + (n - i - k)^2 + 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}]
Formula
a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} (i^2 + k^2 + (n-i-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)).