Geodesic
On coefficients and initial conditions of Somos-6 sequence having rank 3
Dalʹnevostočnyj matematičeskij žurnal, Tome 23 (2023) no. 2, pp. 246-251.

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In the paper we find the conditions for coefficients and initial values of the Somos‑6 sequence, which is the product of two Somos‑4 sequences and has a rank of at most 3. 
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M. A. Romanov. On coefficients and initial conditions of Somos-6  sequence having rank 3. Dalʹnevostočnyj matematičeskij žurnal, Tome 23 (2023) no. 2, pp. 246-251. http://geodesic.mathdoc.fr/item/DVMG_2023_23_2_a9/

[1] M. O. Avdeeva, V. A. Bykovskii, “Giperellipticheskie sistemy posledovatelnostei i funktsii”, Dalnevostochnyi matematicheskii zhurnal, 16:2 (2016), 115–122 | MR | Zbl

[2] A.A. Illarionov, “O posledovatelnosti Somos-4”, DVMZh, 18:2 (2018), 183–188 | MR | Zbl

[3] A.A. Illarionov, “Funktsionalnoe uravnenie i sigma-funktsiya Veiershtrassa”, Funkts. analiz i ego prilozheniya, 50:4 (2016), 43–54 | DOI | MR | Zbl

[4] A.A. Illarionov, “Giperellipticheskie sistemy posledovatelnostei ranga 4”, Matem. sb., 210:9 (2019), 59–88 | DOI | MR | Zbl

[5] Y. N. Fedorov, A. N. W. Hone, “Sigma function solution of the general Somos‐6 recurrence via hyperelleptic Prym varieties”, Journal of Integrable Systems, 1:1 (2016), 1–34 | Zbl

[6] A. N. W. Hone, “Elliptic curves and quadratic recurrence sequences”, Bull. London Math. Soc., 37:2 (2005), 161–171 | DOI | MR | Zbl

[7] R. Shipsey, Elliptic Divisibility Sequences, Goldsmith's University of London, 2000

[8] C. S. Swart, Elliptic curves and related sequences, Royal Holloway and Bedford New College, University of London, 2003

[9] C. S. Swart, A. N. W. Hone, “Integrality and the Laurent phenomenon for Somos 4 and Somos 5 sequences”, Math. Proc. Camb. Philos. Soc., 145:1 (2008), 65–85 | DOI | MR | Zbl

[10] Van der Poorten A. J., Swart C. S., “Recurrence relations for elliptic sequences: every Somos 4 is a Somos $k$”, Bull. London Math. Soc., 38:4 (2006), 546–554 | DOI | MR | Zbl