A369611 - OEIS

%I #18 Jan 28 2024 08:33:10

%S -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 16,17,18,19,20,21,23,24,25,26,28,29,31,32,33,35,37,38,40,41,43,45,47,

%U 48,50,52,54,56,58,59,62,64,66,68,70,72,75,77,79,81,84,86,89

%N Tropical version of Somos-7 sequence A006723.

%C 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 Second difference has period 30.

%H <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 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 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 (Maxima)  N : 7$ 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] ) ),

%o    A[i] : M - A[i - N]

%o )$ A;

%Y Cf. A006723, A220838, A333251, A369113, A368483.

%K sign,easy

%O 0,12

%A _Helmut Ruhland_, Jan 27 2024