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A308253
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Number of integer-sided triangles with perimeter n and nonprime side lengths.
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3
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0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 2, 2, 2, 3, 4, 2, 4, 4, 5, 3, 5, 4, 7, 6, 7, 8, 10, 6, 9, 8, 11, 7, 10, 8, 13, 11, 14, 15, 18, 11, 16, 14, 19, 19, 21, 20, 26, 26, 28, 30, 33, 25, 30, 30, 34, 27, 32, 29, 37, 35, 39, 40, 45, 44, 47, 47, 53
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OFFSET
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1,18
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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)} sign(floor((i+k)/(n-i-k))) * c(i) * c(k) * c(n-i-k), where c(n) = A005171(n).
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MATHEMATICA
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Table[Sum[Sum[(1 - PrimePi[i] + PrimePi[i - 1]) (1 - PrimePi[k] + PrimePi[k - 1]) (1 - PrimePi[n - i - k] + PrimePi[n - i - k - 1]) 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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