Geodesic
On the Somos-4 sequence
Dalʹnevostočnyj matematičeskij žurnal, Tome 18 (2018) no. 2, pp. 183-188

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In 2005 A.N.W. Hone has obtained an explicit formula for Somos-4 sequences in terms of the Weierstrass sigma function. The proof is valid only for sequences without zero terms. We prove that arbitrary sequence satisfying the Somos-4 equation is determined by the same formula iff it satisfies some determinant identity (analogue of the formula of addition). We give examples of sequences that satisfy the Somos-4 equation but do not satisfy the determinant identity. 
@article{DVMG_2018_18_2_a4,
     author = {A. A. Illarionov},
     title = {On the {Somos-4} sequence},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {183--188},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2018_18_2_a4/}
}
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A. A. Illarionov. On the Somos-4 sequence. Dalʹnevostočnyj matematičeskij žurnal, Tome 18 (2018) no. 2, pp. 183-188. http://geodesic.mathdoc.fr/item/DVMG_2018_18_2_a4/