|
EXAMPLE
|
From the table of powers of A(x), we see that
3^n+1 = Sum of coefficients [x^0] through [x^n] in A(x)^n:
A^1 = [1, 3], -3, 9, -36, 162, -783, 3969, -20817, 112023, ...
A^2 = [1, 6, 3], 0, -9, 54, -297, 1620, -8910, 49572, ...
A^3 = [1, 9, 18, 0], 0, 0, -27, 243, -1701, 10935, ...
A^4 = [1, 12, 42, 36, -9], 0, 0, 0, -81, 972, ...
A^5 = [1, 15, 75, 135, 45, -27], 0, 0, 0, 0, ...
A^6 = [1, 18, 117, 324, 324, 0, -54], 0, 0, 0, ...
A^7 = [1, 21, 168, 630, 1071, 567, -189, -81], 0, 0, ...
A^8 = [1, 24, 228, 1080, 2610, 2808, 540, -648, -81], 0, ...
the main diagonal of which is:
[x^n]A(x)^(n+1) = (n+1)*A057083(n) for n>=0.
|