Berlekamp–Massey over $\mathbb{Q}$ applied to the extended sequence yields a minimal recurrence of order exactly 10 with coefficients exactly $[12, -54, 98, 17, -346, 505, -210, -120, 126, -27]$ — identically Barker's 2018 conjecture — and the recurrence holds exactly for every term $11 \le n \le 5000$ (zero failures).