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A236384
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Number of non-congruent integer triangles with base length n whose apex lies on or within a space bounded by a semicircle of diameter n.
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4
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0, 0, 1, 1, 3, 4, 5, 7, 10, 13, 15, 17, 22, 25, 30, 33, 38, 42, 48, 54, 58, 65, 71, 76, 85, 92, 100, 106, 114, 123, 130, 140, 149, 159, 170, 177, 189, 197, 211, 222, 231, 243, 255, 269, 282, 292, 306, 318, 333, 348, 364, 378, 391, 406, 420, 438, 453, 470, 485
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OFFSET
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1,5
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COMMENTS
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Number of integer-sided obtuse or right (non-acute) triangles with largest side n. - Frank M Jackson, Dec 03 2014
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LINKS
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FORMULA
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EXAMPLE
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a(5)=3 as there are 3 non-congruent integer triangles with base length 5 whose apex lies on or within the space bounded by the semicircle of diameter 5. The integer triples are (2,4,5), (3,3,5), (3,4,5).
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MATHEMATICA
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sumtriangles[c_] := (n=0; Do[If[a^2+b^2<=c^2, n++], {b, 1, c}, {a, c-b+1, b}]; n); Table[sumtriangles[m], {m, 1, 200}]
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PROG
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(GeoGebra)
c = Slider(1, 20, 1);
L = Flatten(Sequence(Sequence(((a^2+c^2-(c-a+k)^2)/(2c), ((a+(c-a+k)+c)(a+(c-a+k)-c)(a-(c-a+k)+c)(-a+(c-a+k)+c))^(1/2)/(2c)), a, k, (c+k)/2), k, 1, c));
C = {Circle((c/2, 0), c/2)};
a_n = CountIf(IsInRegion((x(A), y(A)), Element(C, 1)), A, L);
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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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