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Search: id:A119661
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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
1
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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; listen)
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OFFSET
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1,1
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COMMENT
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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
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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
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G. A. Galperin, A. N. Zemliakov, "Mathematical Billiards" (in Russian)
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FORMULA
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a(n) = -IntegerPart[ -Pi/ArcCos[n/(n+1)]].
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MATHEMATICA
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Table[ -IntegerPart[ -Pi/ArcCos[n/(n+1)]], {n, 1, 100}]
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CROSSREFS
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Sequence in context: A075324 A134993 A011375 this_sequence A120196 A120188 A097356
Adjacent sequences: A119658 A119659 A119660 this_sequence A119662 A119663 A119664
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 28 2006
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