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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).
1
1, 1, 5, 12, 22, 34, 50, 65, 78, 78, 86, 78, 78, 65, 50, 34, 22, 12, 5, 1, 1
OFFSET
0,3
EXAMPLE
For 2 vertices, there are 5 different sets:
{10 pairs with norm^2 of sum = 0.000}
{30 pairs with 1.000}
{60, 2.618}
{60, 5.236}
{30, 6.854}
the norm^2 is taken with the side of the pentagons = 1.
And of course 10+30+60+60+30 = 190 = 20 choose 2
CROSSREFS
Sequence in context: A242338 A217649 A333578 * A074376 A293502 A134340
KEYWORD
nonn,fini,full
AUTHOR
N. J. A. Sloane, Oct 06 2007, based on an email message from Wouter Meeussen on Dec 27 2004.
EXTENSIONS
More terms from Wouter Meeussen, Oct 07 2007
STATUS
approved