old seqs related to dodecahedron, help needed
wouter meeussen
wouter.meeussen at pandora.be
Sun Oct 7 12:26:08 CEST 2007
in the cited excel sheet (link is dysfunctional)
for k from (0) to 10:
(1), 1,5,12,22,34,50,65,78,78,86
from k=11 to 20, we should get the same sequence backwards of course.
So it's now a 'fini'.
I had forgotten all about this, the link is
http://users.pandora.be/Wouter.Meeussen/DodecahedralVectorSum.xls
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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