querying multidimensional sequences in OEIS

Marc LeBrun mlb at well.com
Fri Nov 3 22:41:00 CET 2006


 > 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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