
What's the next number in this sequence? - adtac
https://adtac.github.io/blog/post/next-number-in-the-sequence/
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JoeAltmaier
There's a trivial way to generate a machine to come up with polynomial number
sequences. Just write the sequence in a column. Then take the differences
between each entry and the next, and write it to the left. Once that column is
complete, repeat (taking differences between entry and next entry, and write
to the left). When you get down to 1 entry (there is 1 fewer in each column)
just fill that down the column to complete the matrix.

To generate next entries, simply take the last row and add each entry to the
one to the left, and write it below creating a new row. The right column is
your polynomial sequence.

This was used in hardware long ago to generate simple polynomial curves in a
graphics circuit using only cascaded adders.

