
EXAMPLE

The exponent codes of A164092 are:
.
0; (skip as trivial);
1, 1; (creates the 2x2 matrix [w,1/w; 1/w,w](exponents of w = 1 & 1).
2, 0, 2, 0;
3, 1, 1, 1, 1, 3, 1, 1;
4, 3, .0, 2, .0, 2, .0, 2, 0, 2, 4, 2, 0, 2, 0, 2;
...
Exponent codes (above) are generated by adding "1" to each term in nth row bringing down that subset as the first half of the next row. Second half of the next (n+1)th) row is created by reversing the terms of nth row and subtracting "1" from each term. (2, 0, 2, 0) becomes (3, 1, 1, 1) as the first half of the next row. Then append (1, 3, 1, 1), getting (3, 1, 1, 1, 1, 3, 1, 1) as row 3. Let these rows = "A" for each matrix
.
In a 2^n * 2^n matrix with a conventional upper left term of (1,1), place A as the top row and left column. Put leftmost term of A into every (n,n) (i.e. diagonal position). Then, odd columns are circulated from position (n,n) downwards while even columns circulate upwards starting from (n,n). Using A with 8 terms we obtain the following 8x8 matrix:
.
3, 1, 1, 1, 1, 3, 1, 1;
1, 3, 1, 1, 3, 1, 1, 1;
1, 1, 3, 1, 1, 1, 1, 3;
1, 1, 1, 3, 1, 1, 3, 1;
1, 3, 1, 1, 3, 1, 1, 1;
3, 1, 1, 1, 1, 3, 1, 1;
1, 1, 1, 3, 1, 1, 3, 1;
1, 1, 3, 1, 1, 1, 1, 3;
.
The foregoing terms are exponents to w, so our new matrix becomes:
.
1, w, 1/w, w, 1/w, 1, 1/w, w;
w, 1, w, 1/w, 1, 1/w, w, 1/w;
1/w, w, 1, w, 1/w, w, 1/w, 1;
w, 1/w, w, 1, w, 1/w, 1, 1/w;
1/w, 1, 1/w, w, 1, w, 1/w, w;
1, 1/w, w, 1/w, w, 1, w, 1/w;
1/w, w, 1/w, 1, 1/w, w, 1, w;
w, 1/w, 1, 1/w, w, 1/w, w, 1;
.
Let the foregoing matrix = Q, then take Q^2 =
.
1, 2, 4, 2, 4, 8, 4, 2;
2, 1, 2, 4, 8, 4, 2, 4;
4, 2, 1, 2, 4, 2, 4, 8;
2, 4, 2, 1, 2, 4, 8, 4;
4, 8, 4, 2, 1, 2, 4, 2;
8, 4, 2, 4, 2, 1, 2, 4;
4, 2, 4, 8, 4, 2, 1, 2;
2, 4, 8, 4, 2, 4, 2, 1;
.
Following analogous procedures for the 2x2 and 4x4 matrices, those are [ 1, 2; 2,1], and
.
1, 2, 4, 2;
2, 1, 2, 4;
4, 2, 1, 2;
2, 4, 2, 1;
.
Take antidiagonals of the matrices until all terms in each matrix are used.
