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.

0, 1, 1, -8, -10, -14, 17, 15, 15, 7, 0, -7, -6, -6, -6, -7, 19, 19, 20, 22, 25, 20, 16, 12, -18, -22, -27, -34, -33, -33, -34, -36, -12, 38, 63, 62, 63, 66, 70, 67, 66, 66, 40, -12, -37, -37, -38, -40, -34, -28, -23, -19, 12, 16, 20, 25, 30, 26, 23, 20, -10, -13, -16

Offset: 0

Author

Ctibor O. Zizka, Dec 19 2023

Keywords

• sign

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].

Examples

			a(0) = 0; a(1) = 1; a(2) = 1 - 9*floor(median(0,1)) + floor(mean(0,1)) = 1.
		

Links

• Thomas Scheuerle, Scatter plot of a(n) for n = 0..60000

Crossrefs

Cf. A365819, A368274.

Programs

MATLAB

function a = A368280( max_n )
    a = [0 1];
    for n = 3:max_n
        a(n) = a(n-1) - 9*floor(median(a)) + floor(mean(a));
    end
end % Thomas Scheuerle, Dec 19 2023

Formula

a(n) = 0 for n >= 54698. - Thomas Scheuerle, Dec 19 2023