Squaring the plane

An easy method of tiling/squaring the plane with integer squares of sides 1, 2, 3..n^2.
OK, not infinite area, exactly – but a greater area than any specified area, no matter how large – which is what infinite means, in practice, I guess. Seems to work the same for each n^2.
It’s by using an n\times n arrangement of squares, with any odd n, a similar simple arrangement for each one, e.g. with n = 7, 9, 11: (49, 81, 121 squares)

11x11 col compr 3
How to number the squares:
1. Begin at bottom right corner of an n\times n square grid. Number every second square leftwards across the bottom row, in a checkerboard pattern, i.e. 1, (gap), 2, (gap)..etc. Then across second bottom row. Continue R to L across every row. Finish at top left with \frac{n^2+1}{2}.
2. Start at top right, going down the columns, filling the remaining gaps, and moving R to L. i.e. first the rightmost column. Top square is already filled, put \frac{n^2+3}{2} in the second row, the next number in the fourth etc.
Maybe easier to see than explain. e.g. for the 5×5 square:5x5 grid
Squares are arranged with what I call alternating h-lines and v-lines, shown as black lines in the picture. An h-line is a horizontal line segment with two squares on each side of it, a v-line, a vertical line segment with two squares on each side. The arrangement has a h-line on the top left, v-line on the top right.

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