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A119661
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Maximum possible number of a pairwise elastic collisions in a dynamic system of 3 point masses m1,m2,m3 on a line, where m1 = n*m2 = m3.
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0
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3, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| a(n) = N(m1,m2,m3) is independent of initial velocities and coordinates of masses m1,m2,m3. N(m1,m2,m3) = -IntegerPart[ -Pi/ArcCos[Sqrt[m1*m3/((m1+m2)*(m2+m3))]]].
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REFERENCES
| G. A. Galperin, A. N. Zemliakov, "Mathematical Billiards", "KVANT" Library, Issue 77, Moscow, Nauka, 1990, (in Russian). See p. 165.
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LINKS
| G. A. Galperin, A. N. Zemliakov, "Mathematical Billiards" (in Russian)
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FORMULA
| a(n) = -IntegerPart[ -Pi/ArcCos[n/(n+1)]].
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MATHEMATICA
| Table[ -IntegerPart[ -Pi/ArcCos[n/(n+1)]], {n, 1, 100}]
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CROSSREFS
| Sequence in context: A075324 A134993 A011375 * A120196 A196179 A120188
Adjacent sequences: A119658 A119659 A119660 * A119662 A119663 A119664
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KEYWORD
| nonn
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AUTHOR
| Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 28 2006
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