Search: id:A131976
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%I A131976
%S A131976 1,1,5,12,22,34,50,65,78,78,86,78,78,65,50,34,22,12,5,1,1
%N A131976 Let G be the full icosahedral group, of order 120. Let v_1, ..., v_20 
               be the vertices of the dodecahedron. Let S(n) be the set of vectors 
               v_{i_1} + v_{i_2} + ... + v_{i_n} where 1 <= i_1 <= i_2 <= ... <= 
               i_n <= 20. Then a(n) = number of orbits of G on S(n).
%H A131976 Wouter Meeussen, <a href="http://users.pandora.be/Wouter.Meeussen/DodecahedralVectorSum.xls">
               Excel spreadsheet</a>
%e A131976 For 2 vertices, there are 5 different sets:
%e A131976 {10 pairs with norm^2 of sum = 0.000}
%e A131976 {30 pairs with 1.000}
%e A131976 {60, 2.618}
%e A131976 {60, 5.236}
%e A131976 {30, 6.854}
%e A131976 the norm^2 is taken with the side of the pentagons = 1.
%e A131976 And of course 10+30+60+60+30 = 190 = 20 choose 2
%Y A131976 Sequence in context: A097984 A028347 A038794 this_sequence A074376 A134340 
               A000326
%Y A131976 Adjacent sequences: A131973 A131974 A131975 this_sequence A131977 A131978 
               A131979
%K A131976 nonn,fini,full
%O A131976 0,3
%A A131976 N. J. A. Sloane (njas(AT)research.att.com), Oct 06 2007, based on an 
               email message from Wouter Meeussen (wouter.meeussen(AT)pandora.be) 
               on Dec 27 2004.
%E A131976 More terms from Wouter Meeussen (wouter.meeussen(AT)pandora.be), Oct 
               07 2007

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