The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
A unimodal sequence is odd-balanced if: (i) the peak is even and unique, (ii) even parts to the left of the peak are distinct, (iii) even parts to the right of the peak are distinct, (iv) odd parts to the left of the peak are identical to the odd parts to the right of the peak.