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%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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