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

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));
    end
end % Thomas Scheuerle, Dec 19 2023

Crossrefs

Cf. A365819.

Sequence in context: A180131 A257972 A222307 * A175838 A347272 A097960

Adjacent sequences: A368271 A368272 A368273 * A368275 A368276 A368277

Keyword

sign

Author

Ctibor O. Zizka, Dec 19 2023

Status

approved