New sources of inspiration?

karttu at karttu at
Sat Jun 3 23:38:10 CEST 2000

Neil wrote: 
> - quite often when i look at a physics journal i see sequences that should 
> be in the table.

How about biology then? I.e., I was just searching information about
how icosahedral viruses (virii) are formed, when I found this page:

Here's a quote:

  The theoretical basis for the structure of isometric viruses was put on
  a firm foundation by Caspar and Klug (1962) with their concept of
  identical elements in quasi-equivalent environments. They defined all
  possible polyhedra in terms of structure units. The icosahedron itself
  has 20 equilateral triangular facets and therefore 20T structure units
  where T is the TRIANGULATION NUMBER given by the rule: 
  T=Pf^2 where P can be any number of the series 1,3,7,13,19,21,31 ..
  (=h^2 + hK +K^2), for all pairs of integers, h and K having no common factor)
  and f is any integer. 
  Morphological units can be clustered as 20T trimers, 30T dimers or
  separated as 60T monomers. The number of morphological units that
  would be produced by a clustering into hexamers and pentamers can
  be calculated as follows: There are 10(T-1) hexamers plus 12.
  (and only 12) pentamers. 

  Caspar and Klug (1962) claimed that most icosahedral viruses fall into
  2 classes:- P=1 and P=3; and that all deltahedra for which P=>7 are skew,
  and therefore exist in right and left- handed forms.
  ... etc.

Sequence given seems to be either A034017 or A034021.
(Does "primitively represented by x^2+xy+y^2" mean just that gcd(x,y) =1 ?
In that case it's the latter sequence I guess).

There are lots of discrete mathematics involved in Computational Biology.

(I don't mean with this that next everybody should submit his own genome
encoded in base-4 into EIS, there are other databases for that.)


Antti Karttunen
E-mail: karttu at

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