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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

%I

%S 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,

%T 12,12,12,12,13,13,13,13,13,14,14,14,14,14,14,15,15,15,15,15,15,15,16,

%U 16,16,16,16,16,17,17,17,17,17,17,17,18,18,18,18,18,18,18,18,19,19,19,19

%N 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.

%C 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))]]].

%D G. A. Galperin, A. N. Zemliakov, "Mathematical Billiards", "KVANT" Library, Issue 77, Moscow, Nauka, 1990, (in Russian). See p. 165.

%H G. A. Galperin, A. N. Zemliakov, <a href="http://ilib.mccme.ru/djvu/bib-kvant/billiards.htm">"Mathematical Billiards"</a> (in Russian)

%F a(n) = -IntegerPart[ -Pi/ArcCos[n/(n+1)]].

%t Table[ -IntegerPart[ -Pi/ArcCos[n/(n+1)]],{n,1,100}]

%K nonn

%O 1,1

%A _Alexander Adamchuk_, Jul 28 2006

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