# Fractal Pattern from Queen's Move Construction

This question relates to the OEIS sequence A279212.

Fill an array by antidiagonals upwards; in the top left cell enter $$a(0)=1$$; thereafter, in the $$n$$-th cell, enter the sum of the entries of those earlier cells that can be seen from that cell...

Note: "that can be seen from" means "that are on the same row, column, diagonal, or antidiagonal as." Basically, you're adding up previous terms in cells to which a queen could move on a chessboard.

Here's an animated example that shows how the sequence is built:

My friend Peter Kagey and I have been thinking about the parity of the terms of sequence and have created a bitmap to represent our results. In this bitmap, white cells represent odd values, and black cells represent even values. Click the image for a higher-resolution version with the first $$2^{12}$$ columns and $$2^{13}$$ rows.

We think that the resulting "parity map" of A279212 has interesting structure, and we wonder whether this pattern has a name and/or has been studied before.

• Thinking of this using generating functions, I think there's a more "local" condition controlling the parity map. This comment space is a bit short, but I think that if you overlay the grid prntscr.com/rt8dow onto any position of the parity map, the sum of the entries denoted $+$ will be 0 mod 2. This suggests that if you know the first three columns and first two rows, you could write an explicit mod 2 generating function for this array [Sorry for all the edits, was trying to get a table to show up in this comment] Apr 5, 2020 at 2:17