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A369113 Tropical version of Somos-6 sequence A006722.

%I A369113 #16 May 30 2025 03:15:10
%S A369113 -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 A369113 21,22,24,25,27,29,30,32,34,36,38,39,42,44,46,48,50,53,55,57,60,62,65,
%U A369113 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 A369113 Tropical version of Somos-6 sequence A006722.
%C A369113 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 A369113 Second difference has period 20.
%H A369113 <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 A369113 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 A369113 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 A369113 (Maxima)  N : 6$ Len : 50$  /* tropical version of Somos-N, 2 <= N <= 7, Len = length of the calculated list */
%o A369113 NofRT : floor (N / 2)$  /* number of terms in a Somos-N recurrence */
%o A369113 A : makelist (0, Len)$  A[1] : -1$ for i: 2 thru N do ( A[i] : 0 )$
%o A369113 for i: N + 1 thru Len do (
%o A369113    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 A369113 )$ A;
%Y A369113 Cf. A006722.
%K A369113 sign,easy
%O A369113 0,10
%A A369113 _Helmut Ruhland_, Jan 13 2024