A369113 - OEIS

%I #13 Jan 25 2024 16:17:23

%S -1,0,0,0,0,0,1,1,1,2,2,3,3,4,5,5,6,7,8,9,9,11,12,13,14,15,17,18,19,

%T 21,22,24,25,27,29,30,32,34,36,38,39,42,44,46,48,50,53,55,57,60,62,65,

%U 67,70,73,75,78,81,84,87,89,93,96,99,102,105,109,112,115,119,122,126,129,133,137,140,144,148,152

%N Tropical version of Somos-6 sequence A006722.

%C 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).

%C Second difference has period 20.

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,0,-1,0,0,-1,1)

%F 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.

%F 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

%o (Maxima)  N : 6$ Len : 50$  /* tropical version of Somos-N, 2 <= N <= 7, Len = length of the calculated list */

%o NofRT : floor (N / 2)$  /* number of terms in a Somos-N recurrence */

%o A : makelist (0, Len)$  A[1] : -1$ for i: 2 thru N do ( A[i] : 0 )$

%o for i: N + 1 thru Len do (

%o    M : minf, for j : 1 thru NofRT do ( M : max ( M, A[i - j] + A[i - N + j] ) ),     A[i] : M - A[i - N]

%o )$ A;

%Y Cf. A006722.

%K sign,easy

%O 0,10

%A _Helmut Ruhland_, Jan 13 2024