OEIS for Doubly Indexed Sequences

Question

Is there an OEIS-like database for doubly indexed sequences? I feel like such a database would be extremely useful for mathematicians, and would be surprised if there wasn't one, but I can't seem to find it.

Answer 1

In cases where a doubly indexed "sequence" is needed to be stored, it is stored by antidiagonals in OEIS: from top right to bottom left.

E.g. http://oeis.org/A061554 is an asymmetric example which highlights how it is stored.

$$\begin{array}{cccccccccc} 1 & \color{purple} 1 & \color{red} 2 & \color{blue} 3 & \color{green} 6 & \color{orange}{10} & 20 & 35 & 70 & 126 \\ \color{purple} 1 & \color{red} 1 & \color{blue} 3 & \color{green} 4 & \color{orange}{10} & 15 & 35 & 56 & 126 & 210 \\ \color{red} 1 & \color{blue} 1 & \color{green} 4 & \color{orange} 5 & 15 & 21 & 56 & 84 & 210 & 330 \\ \color{blue} 1 & \color{green} 1 & \color{orange} 5 & 6 & 21 & 28 & 84 & 120 & 330 & 495 \\ \color{green} 1 & \color{orange} 1 & 6 & 7 & 28 & 36 & 120 & 165 & 495 & 715 \\ \color{orange} 1 & 1 & 7 & 8 & 36 & 45 & 165 & 220 & 715 & 1001 \\ 1 & 1 & 8 & 9 & 45 & 55 & 220 & 286 & 1001 & 1365 \\ 1 & 1 & 9 & 10 & 55 & 66 & 286 & 364 & 1365 & 1820 \\ 1 & 1 & 10 & 11 & 66 & 78 & 364 & 455 & 1820 & 2380 \\ 1 & 1 & 11 & 12 & 78 & 91 & 455 & 560 & 2380 & 3060 \end{array}$$

Answer 2

I have encountered several double indexed sequences within the OEIS. They are given in triangular / diagonal enumeration (search "diagonal").

(Why this works: $\mbox{card}(\mathbb{N}^n) = \mbox{card}(\mathbb{N})$, see Pairing Function)

It is mentioned in the hints section as well (link hints).

And there is a section in the demos (link demos).

Some of these series have a web link as special keyword in their ${\rm \small K{\tiny EYWORD}}$ section: tabl from A055830

Which gives renderings of the sequence as several kind of arrays.

                                    1   
                                1       0   
                            2       1       0   
                        3       3       1       0   
                    5       7       4       1       0   
                8       15      12      5       1       0   
            13      30      31      18      6       1       0

As stated in the hints section you can search for them by entering diagonals, rows or columns.