[seqfan] Re: Polycubes and canonical order of k-tuples of nonnegative integers

[Arthur O'Dwyer]

On Sat, Aug 19, 2023 at 1:25 PM John Mason <masonmilan33 at gmail.com> wrote:

> Hi
> I am not sure I understand the problem.
>

IIUC, Pontus is looking at
https://oeis.org/A246521 — "List of free polyominoes in binary coding"
which is an irregular table with row lengths
https://oeis.org/A000105 — "Number of free polyominoes with n cells"
A246521 isn't really a sequence of *numbers*; it's a sequence of
*polyominoes*
▖,▄,▄▖,▙,▄▄,▙▖,▟▖,▜▖, ...
which in order to be entered into OEIS had to be encoded as integers in a
specific conventional way (which is documented in the "Example" on
A246521). For example, "11" doesn't mean eleven, it means ▄▖; "15" doesn't
mean fifteen, it means ▙; and so on.

Pontus is asking what's the analogous specific conventional way (if any) to
encode *polycubes* as integers.
(The polyomino-encoding method reduces to "What's the conventional way to
map $\N\times\N \rarrow \N$?" Therefore Pontus phrased his original
question as "What's the conventional way to map $\N^3 \rarrow \N$?")

–Arthur