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, 5, 12, 22, 34, 50, 65, 78, 78, 86, 78, 78, 65, 50, 34, 22, 12, 5, 1, 1

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Wouter Meeussen, Excel spreadsheet

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

Adjacent sequences: A131973 A131974 A131975 * A131977 A131978 A131979

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