The minimal linear recurrence of the odd branch has order 8 with integer coefficients $[4, -2, -3, -5, 3, 4, 1, -1]$ (Berlekamp–Massey on 40 terms, verified exactly on 140 further terms); the even branches have minimal orders 34 ($n \equiv 0 \bmod 4$) and 35 ($n \equiv 2 \bmod 4$), determined by Berlekamp–Massey over two independent primes with identical results on 375 terms per branch from the 54-state pair transfer.