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Combinatorics International audience Let (w_n)0 < n be the sequence known as Integer Sequence A047749 In this paper, we show that the integer w_n enumerates various kinds of symmetric structures of order two. We first consider ternary trees having a reflexive symmetry and we relate all symmetric combinatorial objects by means of bijection. We then generalize the symmetric structures and correspondences to an infinite family of symmetric objects.doi:10.46298/dmtcs.420 fatcat:lm56ay5xdbfbpblwwpkd6aooni