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We study Olshanski twisted Yangian based models, known as one-dimensional"soliton non-preserving" open spin chains, by means of the algebraic Betheansatz. The even case, when the underlying bulk Lie algebra is$\mathfrak{gl}_{2n}$, was studied in arXiv:1710.08409. In the present work, wefocus on the odd case, when the underlying bulk Lie algebra is$\mathfrak{gl}_{2n+1}$. We present a more symmetric form of the trace formulafor Bethe vectors. We use the composite model approach and$Y(\mathfrak{gl}_n)$-type recurrence relations to obtain recurrence relationsfor twisted Yangian based Bethe vectors, for both even and odd cases.

Bethe vectors and recurrence relations for twisted Yangian based models