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 A119661 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. 0
 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; text; internal format)
 OFFSET 1,1 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))]]]. REFERENCES G. A. Galperin, A. N. Zemliakov, "Mathematical Billiards", "KVANT" Library, Issue 77, Moscow, Nauka, 1990, (in Russian). See p. 165. LINKS G. A. Galperin, A. N. Zemliakov, "Mathematical Billiards" (in Russian) FORMULA a(n) = -IntegerPart[ -Pi/ArcCos[n/(n+1)]]. MATHEMATICA Table[ -IntegerPart[ -Pi/ArcCos[n/(n+1)]], {n, 1, 100}] CROSSREFS Sequence in context: A075324 A134993 A011375 * A120196 A196179 A120188 Adjacent sequences:  A119658 A119659 A119660 * A119662 A119663 A119664 KEYWORD nonn AUTHOR Alexander Adamchuk, Jul 28 2006 STATUS approved

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