"tabf", new keyword

David W. Wilson wilson at cabletron.com
Mon Jul 26 18:58:48 CEST 1999

IMHO, the "tabl", "tabf", "tabh", ad infinitum approach to dealing with
tables is moving in a bad direction, and will not do service to the
database in the long run.  I propose the following solution to the
table problem that deals with the real weakness, which is the indexing

My proposal is to modify the current %O entry to specify of one or more
index sequences.  For instance, the %O line of A000040 (the prime
numbers) would become:

%O A000040 A000027

This says that A000040 is indexed on A000027 (the nonnegative integers).
Thus we have

n    = A000027   1   2   3   4   5   6   7 ...
a(n) = A000040   2   3   5   7  11  13  17 ...

This is much prettier and more general that the current scheme, which
allows only consecutive indices.  For instance, we can now express that
A003649 is indexed on the squarefrees by stating:

%O A003649 A005117

For tables, we give a %O line with two index sequences.  For instance:

%O A007318 A003056 A002262


x      = A003056   0   1   1   2   2   2   3 ...
y      = A002262   0   0   1   0   1   2   0 ...
a(x,y) = A007318   1   1   1   1   2   1   1 ...

This approach allows us to build free-form tables of any dimension.  It
transforms the integer sequence database to an integer function database,
which is really what we want if we are including tables.

Using this approach, it is easy to tell whether we are dealing with a
sequence or with a higher-dimensional table.

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