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A368280 a(0) = 0, a(1) = 1, for n >= 2, a(n) = a(n - 1) - 9*floor(median(a)) + floor(mean(a)). Median(a) and mean(a) are respectively the median and mean of all previous terms.

%I A368280 #21 Dec 31 2023 00:11:28
%S A368280 0,1,1,-8,-10,-14,17,15,15,7,0,-7,-6,-6,-6,-7,19,19,20,22,25,20,16,12,
%T A368280 -18,-22,-27,-34,-33,-33,-34,-36,-12,38,63,62,63,66,70,67,66,66,40,
%U A368280 -12,-37,-37,-38,-40,-34,-28,-23,-19,12,16,20,25,30,26,23,20,-10,-13,-16
%N A368280 a(0) = 0, a(1) = 1, for n >= 2, a(n) = a(n - 1) - 9*floor(median(a)) + floor(mean(a)). Median(a) and mean(a) are respectively the median and mean of all previous terms.
%C A368280 Empirically the system a(0) = 0, a(1) = 1, a(n) = a(n - 1) + A*floor(median(a)) + B*floor(mean(a)) shows five different forms of behavior which are specified by the parameters A and B: exponential growth (e.g., A = 1, B = 1), exponential decline (e.g, A = -2, B = 3), periodic (e.g., A = -4, B = 3), quasi-periodic (e.g., A = -9, B = -9), and chaotic (e.g., A = 2, B = -1). Trials were computed for A, B from [-20, 20] and n from [0, 4*10^4].
%H A368280 Thomas Scheuerle, <a href="/A368280/a368280.png">Scatter plot of a(n) for n = 0..60000</a>
%F A368280 a(n) = 0 for n >= 54698. - _Thomas Scheuerle_, Dec 19 2023
%e A368280 a(0) = 0; a(1) = 1; a(2) = 1 - 9*floor(median(0,1)) + floor(mean(0,1)) = 1.
%o A368280 (MATLAB)
%o A368280 function a = A368280( max_n )
%o A368280     a = [0 1];
%o A368280     for n = 3:max_n
%o A368280         a(n) = a(n-1) - 9*floor(median(a)) + floor(mean(a));
%o A368280     end
%o A368280 end % _Thomas Scheuerle_, Dec 19 2023
%Y A368280 Cf. A365819, A368274.
%K A368280 sign
%O A368280 0,4
%A A368280 _Ctibor O. Zizka_, Dec 19 2023