OFFSET
0,4
COMMENTS
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].
LINKS
Thomas Scheuerle, Plot of a(n) for n = 0..10000.
Thomas Scheuerle, Plot of a(n) for n = 0..100000.
EXAMPLE
a(0) = 0; a(1) = 1; a(2) = 1 - 6*floor(median(0,1)) - 9*floor(mean(0,1)) = 1.
PROG
(MATLAB)
function a = A368274( max_n )
a = [0 1];
for n = 3:max_n
a(n) = a(n-1) - 6*floor(median(a)) - 9*floor(mean(a));
end
end % Thomas Scheuerle, Dec 19 2023
CROSSREFS
KEYWORD
sign
AUTHOR
Ctibor O. Zizka, Dec 19 2023
STATUS
approved