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1 - 2 of 2 for Cyclotomic

The series has an accumulation of poles on the circle Abs[a] 2 1 ; the coefficient of x m turns out to have denominator
2^(m - DigitCount[m, 2, 1]) Apply[Times, Table[Cyclotomic[s, a]^Floor[(m - 1)/s], {s, m - 1}]]
For other iterated maps general formulas also seem rare.

For a register of size n the maximal period of 2 n -1 is obtained whenever x n + Apply[Plus, x taps - 1 ] is one of the EulerPhi[2 n - 1]/n primitive polynomials that appear in Factor[Cyclotomic[2 n - 1, x], Modulus 2] .