[seqfan] Re: A063116

[Neil Sloane]

Returning to A063116, the formula conjectured by Colin Barker is surely
correct,
since a basis for these vector spaces (of cusp forms) can be worked out
explicitly.
MAGMA is very good at this kind of calculation.

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com



On Wed, Aug 21, 2019 at 3:39 PM David Sycamore via SeqFan <
seqfan at list.seqfan.eu> wrote:

> Hello Seqfans,
>
> The Name of the above sequence says:
>
> “Dimension of the space of weight 2n cusp forms for Gamma_0(48).”
>
> (which means nothing to me...).
>
> Data: 3,18,34,66,82,98,114,130,146,162....
>
> Can anyone please explain what is meant by the Name? There is a link
> entitled “Dimensions of the spaces S_k(Gamma_0(N))” but it leads to a
> message saying “Sorry, the website....cannot be found”. Also there are no
> Comments or examples given.
>
> A formula a(n)=2(8n-7) is conjectured, which seems to work.
>
> Unless I am mistaken another possible formula for these terms could be:
>
> a(n)= A(B(n-1)+1) - A(B(n-2)+1) , for n>1
>
> Where A is A000217 and B is A016813.
>
> Any explanation or comments?
>
> Cheers,
>
> David.
>
>
>
>
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>