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A308278 Take all the integer-sided triangles with perimeter n and square number sides a, b, and c such that a <= b <= c. a(n) is the sum of all the b's. 0
0, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 9, 0, 0, 9, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 16, 9, 0, 16, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 16, 0, 0, 25, 0, 0, 25, 0, 0, 16, 0, 25, 0, 0, 0, 0, 0, 0, 25, 0, 0, 0, 0, 0, 0, 36, 0, 25, 36, 25, 0, 0, 0, 36, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,9
LINKS
Wikipedia, Integer Triangle
FORMULA
a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} sign(floor((i+k)/(n-i-k+1))) * A010052(i) * A010052(k) * A010052(n-i-k) * i.
MATHEMATICA
Table[Sum[Sum[i (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
Sequence in context: A224861 A050443 A306770 * A308277 A278216 A036480
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, May 18 2019
STATUS
approved

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Last modified March 29 10:44 EDT 2024. Contains 371268 sequences. (Running on oeis4.)