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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.

0, 1, 1, -5, 4, -2, 7, 1, -5, -11, -2, 7, 16, 10, -5, -20, -11, -2, 13, 22, 22, 7, -17, -32, -23, -14, 10, 28, 28, 22, 7, -8, -23, -29, -20, -11, 4, 13, 22, 16, 10, 4, -2, -8, -14, -20, -11, -2, 13, 22, 22, 16, 10, -5, -20, -26, -26, -17, -2, 19, 34, 34, 34, 19

(list; graph; refs; listen; history; text; internal format)

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

Table of n, a(n) for n=0..63.

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));