old seqs related to dodecahedron, help needed

[wouter meeussen]

for A131977 (Analogue of A131976 for the icosahedron)
I find
(1), 1, 3, 5, 8, 8, 12, ...and down again... ( 8, 8, 5, 3, 1, (1) )

the norms are:
{1/8*(5 + Sqrt[5])}

{0, 1, 1/2*(3 + Sqrt[5])}

{3/8*(3 - Sqrt[5]), 1/8*(5 + Sqrt[5]), 1/8*(13 + Sqrt[5]), 3/8*(7 +
3*Sqrt[5]), 1/8*(17 + 5*Sqrt[5])}

{0, 1, 2, 1/2*(3 - Sqrt[5]), 1/2*(3 + Sqrt[5]), 3 + Sqrt[5], 1/4*(3 +
Sqrt[5])^2, 1/2*(5 + Sqrt[5])}

{1/8*(17 - 3*Sqrt[5]), 3/8*(3 - Sqrt[5]), 1/8*(5 + Sqrt[5]), 5/8*(5 +
Sqrt[5]), 1/8*(13 + Sqrt[5]), 3/8*(7 + 3*Sqrt[5]),   1/8*(17 + 5*Sqrt[5]),
1/8*(33 + 13*Sqrt[5])}

{0, 1, 2, 3, 1/2*(3 - Sqrt[5]), 1/2*(5 - Sqrt[5]), 1/2*(3 + Sqrt[5]), 3 +
Sqrt[5], 3/2*(3 + Sqrt[5]), 1/4*(3 + Sqrt[5])^2,   1/2*(5 + Sqrt[5]), 5 +
2*Sqrt[5]}

Wouter.

----- Original Message ----- 
From: "N. J. A. Sloane" <njas at research.att.com>
To: <njas at research.att.com>; <wouter.meeussen at vandemoortele.com>;
<wouter.meeussen at pandora.be>; <seqfan at ext.jussieu.fr>
Sent: Saturday, October 06, 2007 10:23 PM
Subject: old seqs related to dodecahedron, help needed


>
> Dear Seqfans,  I have about 900 old emails with suggestions
> for sequences in them.  The earliest one was from Wouter,
> and I have based two sequences on it, see below.
> Could someone compute more terms?  This should be easy
> with Magma, I think.
> Neil
>
> %I A131976
> %S A131976 1,1,5
> %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">Exc
el 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
> %O A131976 0,3
> %K A131976 nonn,bref,more
> %A A131976 njas, Oct 06 2007, based on an email message from Wouter
Meeussen (wouter.meeussen(AT)pandora.be) on Dec 27 2004.
>
> %I A131977
> %S A131977 1,1,4
> %N A131977 Analogue of A131976 for the icosahedron.
> %H A131977 Wouter Meeussen, <a
href="http://users.pandora.be/Wouter.Meeussen/DodecahedralVectorSum.xls">Exc
el spreadsheet</a>
> %O A131977 0,3
> %K A131977 nonn,bref,more
> %A A131977 njas, Oct 06 2007, based on an email message from Wouter
Meeussen (wouter.meeussen(AT)pandora.be) on Dec 27 2004.
>
>
>
>
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