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A308097
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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.
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0
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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
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OFFSET
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1,12
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LINKS
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FORMULA
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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)).
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MATHEMATICA
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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}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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