Tropical sequences associated with Somos sequences

Since the seminal note published by M. Somos in 1989, a great deal of attention specialists number theory and adjacent areas are attracted nonlinear sequences that satisfy quadratic recurrence relation. At same time, special is paid to construction integer their Laurent property with respect initial values coefficients recurrence. In fundamental works Robinson, Fomin Zelevinsky Somos-k sequence for k = 4, 5, 6, 7 was proved. Hone, representations Somos-4 5 were found via Weierstrass sigma function on elliptic curves, 6 Klein hyperelliptic curve genus It should also be noted naturally arise cryptosystems curves over finite field. This explained reason addition theorems hold mentioned above, they when calculating multiple points curves. For 7, polynomials variables ordinary Therefore, these can written as an irreducible fraction polynomial numerator variables. this case, denominator monomial Using tropical functions, we prove degrees above represented order index element sequence, whose free terms periodic rational numbers. Moreover, each case periods free  explicitly