cp's OEIS Frontend

A368274 a(0) = 0, a(1) = 1, for n >= 2, a(n) = a(n-1) - 6*floor(median(a)) - 9*floor(mean(a)). Median(a) and mean(a) are respectively the median and mean of all previous terms.

%I A368274 #17 Dec 31 2023 00:11:07
%S A368274 0,1,1,-5,4,-2,7,1,-5,-11,-2,7,16,10,-5,-20,-11,-2,13,22,22,7,-17,-32,
%T A368274 -23,-14,10,28,28,22,7,-8,-23,-29,-20,-11,4,13,22,16,10,4,-2,-8,-14,
%U A368274 -20,-11,-2,13,22,22,16,10,-5,-20,-26,-26,-17,-2,19,34,34,34,19
%N A368274 a(0) = 0, a(1) = 1, for n >= 2, a(n) = a(n-1) - 6*floor(median(a)) - 9*floor(mean(a)). Median(a) and mean(a) are respectively the median and mean of all previous terms.
%C A368274 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 A368274 Thomas Scheuerle, <a href="/A368274/a368274.png">Plot of a(n) for n = 0..10000</a>.
%H A368274 Thomas Scheuerle, <a href="/A368274/a368274_1.png">Plot of a(n) for n = 0..100000</a>.
%e A368274 a(0) = 0; a(1) = 1; a(2) = 1 - 6*floor(median(0,1)) - 9*floor(mean(0,1)) = 1.
%o A368274 (MATLAB)
%o A368274 function a = A368274( max_n )
%o A368274     a = [0 1];
%o A368274     for n = 3:max_n
%o A368274         a(n) = a(n-1) - 6*floor(median(a)) - 9*floor(mean(a));
%o A368274     end
%o A368274 end % _Thomas Scheuerle_, Dec 19 2023
%Y A368274 Cf. A365819.
%K A368274 sign
%O A368274 0,4
%A A368274 _Ctibor O. Zizka_, Dec 19 2023