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 A308064 Number of triangles with perimeter n whose side lengths are square numbers. 4
 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,99 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 FORMULA a(n) = Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} sign(floor((i+k)/(n-i-k+1))) * c(i) * c(k) * c(n-i-k), where c(n) is the characteristic function of squares (A010052). MAPLE N:= 100: V:= Vector(N): for a from 1 to floor(sqrt(N/3)) do for b from a to floor(sqrt((N-a^2)/2)) do R:= map(c -> a^2 + b^2 + c^2, [\$b .. floor(sqrt(min(a^2+b^2-1, N-a^2-b^2)))]); V[R]:= map(`+`, V[R], 1); od od: convert(V, list); # Robert Israel, Jan 01 2020 MATHEMATICA Table[Sum[Sum[(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 Cf. A010052. Sequence in context: A374276 A037281 A143241 * A258825 A361162 A118626 Adjacent sequences: A308061 A308062 A308063 * A308065 A308066 A308067 KEYWORD nonn AUTHOR Wesley Ivan Hurt, May 10 2019 STATUS approved

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Last modified August 13 15:25 EDT 2024. Contains 375142 sequences. (Running on oeis4.)