OFFSET
0,10
COMMENTS
Given the Somos-6 sequence with variables s(1), s(2), s(3), s(4), s(5), s(6) and recursion s(n) = (s(n-1)*s(n-5) + (s(n-2)*s(n-4) + s(n-3)^2)/s(n-6), then s(n) is a Laurent polynomial in the variables with the numerator being irreducible and the denominator is Product_{k=0..5} s(k+1)^a(n-k).
Second difference has period 20.
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,0,-1,0,0,-1,1)
FORMULA
a(n) = max( a(n-1) + a(n-5), a(n-2) + a(n-4), 2*a(n-3) ) - a(n-6) for all n in Z.
G.f.: (-1 + x + x^4)/((1 - x)^3*(1 + x)*(1 + x^2)*(1 + x + x^2 + x^3 + x^4)). - Stefano Spezia, Jan 14 2024
PROG
(Maxima) N : 6$ Len : 50$ /* tropical version of Somos-N, 2 <= N <= 7, Len = length of the calculated list */
NofRT : floor (N / 2)$ /* number of terms in a Somos-N recurrence */
A : makelist (0, Len)$ A[1] : -1$ for i: 2 thru N do ( A[i] : 0 )$
for i: N + 1 thru Len do (
M : minf, for j : 1 thru NofRT do ( M : max ( M, A[i - j] + A[i - N + j] ) ), A[i] : M - A[i - N]
)$ A;
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Helmut Ruhland, Jan 13 2024
STATUS
approved