querying multidimensional sequences in OEIS
Jon Awbrey
jawbrey at att.net
Fri Nov 3 22:51:00 CET 2006
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you might get some ideas from looking at the
tables of "primal codes" or "primal functions"
that I compiled, for instance, here:
http://stderr.org/pipermail/inquiry/2005-July/002846.html
ja
Marc LeBrun wrote:
>
> > I have a number of multidimensional sequences in mind that I'd like to
> > see in OEIS. E.g.: the coefficients of incomplete Bell polynomials:
>
> Two possible ways to submit sequences of tuples T(1),T(2),...
> where T(i)=[T(i,1),T(i,2),...] are:
>
> A. Define a traversal order by a map (i,j) <--> n and set a(n) = T(i,j).
> This gives the tabl/tabf style of entry.
>
> B. Encode each tuple as a single number, say by using it as factor
> exponents: T(i) --> 2^T(i,1) * 3^T(i,2) * 5^T(i,3) *...
>
> For example, for Pascal's triangle
>
> A: 1; 1, 1; 1, 2, 1; 1, 3, 3, 1;...
>
> B: 2, 6, 90, 47250,...
>
> However there are a variety of possible ways to do these things--for example
> you might subtract 1 from all the Pascal exponents, B': 1, 1, 3, 225,...
>
> Or traverse in the order (1,1), (2,1), (1,2), (3,1), (1,3), (2,2), (1,4),...
> which recursively interleaves sequences instead of the usual diagonalizing.
>
> But this sort of thing can also be abused to breed swarms of silly sequences,
> so it should be well-motivated.
>
> It's nicest to use familiar schemes (eg as Frank noted for partitions).
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