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A369611 Tropical version of Somos-7 sequence A006723.

%I A369611 #18 Jan 28 2024 08:33:10
%S A369611 -1,0,0,0,0,0,0,1,1,1,1,2,2,3,3,3,4,5,5,6,6,7,8,9,9,10,11,12,13,14,14,
%T A369611 16,17,18,19,20,21,23,24,25,26,28,29,31,32,33,35,37,38,40,41,43,45,47,
%U A369611 48,50,52,54,56,58,59,62,64,66,68,70,72,75,77,79,81,84,86,89
%N A369611 Tropical version of Somos-7 sequence A006723.
%C A369611 Given the Somos-7 sequence with variables s(1), s(2), s(3), s(4), s(5), s(6), s(7) and recursion s(n) = (s(n-1)*s(n-6) + s(n-2)*s(n-5) + s(n-3)*s(n-4))/s(n-7), then s(n) is a Laurent polynomial in the variables with the numerator being irreducible and the denominator is Product_{k=0..6} s(k+1)^a(n-k).
%C A369611 Second difference has period 30.
%H A369611 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,0,0,0,-1,-1,0,1).
%F A369611 a(n) = max( a(n-1) + a(n-6), a(n-2) + a(n-5), a(n-4) + a(n-3) ) - a(n-7) for all n in Z.
%F A369611 G.f.: ( 1-x^2-x^3 ) / ( (1+x)*(1+x+x^2)*(x^4+x^3+x^2+x+1)*(x-1)^3 ). - _R. J. Mathar_, Jan 28 2024
%o A369611 (Maxima)  N : 7$ Len : 50$  /* tropical version of Somos-N, 2 <= N <= 7, Len = length of the calculated list */
%o A369611 NofRT : floor (N / 2)$  /* number of terms in a Somos-N recurrence */
%o A369611 A : makelist (0, Len)$  A[1] : -1$ for i: 2 thru N do ( A[i] : 0 )$
%o A369611 for i: N + 1 thru Len do (
%o A369611    M : minf, for j : 1 thru NofRT do ( M : max ( M, A[i - j] + A[i - N + j] ) ),
%o A369611    A[i] : M - A[i - N]
%o A369611 )$ A;
%Y A369611 Cf. A006723, A220838, A333251, A369113, A368483.
%K A369611 sign,easy
%O A369611 0,12
%A A369611 _Helmut Ruhland_, Jan 27 2024