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A070093
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Number of acute integer triangles with perimeter n.
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15
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0, 0, 1, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 2, 4, 3, 5, 4, 5, 5, 5, 6, 6, 6, 7, 7, 9, 8, 10, 9, 10, 10, 11, 12, 12, 12, 14, 13, 16, 14, 17, 16, 17, 18, 18, 20, 20, 20, 22, 22, 24, 23, 25, 26, 26, 27, 28, 30, 30, 29, 32, 31, 35, 33, 36, 36, 38, 39, 40, 40
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,9
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COMMENTS
| An integer triangle [A070080(k)<=A070081(k)<=A070082(k)] is acute iff A070085(k)>0;
a(n) = A005044(n) - A070101(n) - A024155(n);
a(n) = A042154(n) + A070098(n).
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LINKS
| Eric Weisstein's World of Mathematics, Acute Triangle.
R. Zumkeller, Integer-sided triangles
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EXAMPLE
| For n=9 there are A005044(9)=3 integer triangles: [1,4,4], [2,3,4] and [3,3,3]; two of them are acute, as 2^2+3^2<16=4^2, therefore a(9)=2.
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CROSSREFS
| Cf. A070094, A070095, A070118.
Sequence in context: A178930 A126759 A029348 * A174931 A058744 A185617
Adjacent sequences: A070090 A070091 A070092 * A070094 A070095 A070096
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KEYWORD
| nonn
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 05 2002
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