I have a sequence A with the fractal pattern that the innermost values x, where length(x) = length(A)/2, has sum(x) = sum(A)/2. Also this is a fractal pattern so that for sequence x with the fractal pattern that the innermost values y, where length(y) = length(x)/2, has sum(y) = sum(x)/2. This continues as long as the innermost values length is divisible by 2. Example:

A = 31,18,37,24,27,46,33,36,23,-6,-3,16,19,38,41,12,-1,2,-11,8,11,-2,17,4 x = 33,36,23,-6,-3,16,19,38,41,12,-1,2 y = -6,-3,16,19,38,41

A(length)=24 A(sum)=420 x(length)=12 x(sum)=210 y(length)=6 y(sum)=105

I have a list of other constraints to aid in this: for a sequence of integers z that is 48 values in length, for values x and y, at positions a and b, x+y=35, where a=48-(b-1), partitioning z into 16 sections each with 3 consecutive values from z, and summing the pieces giving 3 final values, M,N,O, ie M is a sum of values at position 1,4,7,10,13,…46, where:

M < N < O, and O – N = N – M, and N -M is a power of 2. How many possible integer sequences z exist?

z=27, -18, 1, 4, 23, 26, 13, 32, 19, 22, 41, 44, 31, 18, 37, 24, 27, 46, 33, 36, 23, -6, -3, 16, 19, 38, 41, 12, -1, 2, -11, 8, 11, -2, 17, 4, -9, -6, 13, 16, 3, 22, 9, 12, 31, 34, 53, 8. Also A is a subset of z.

In this example: M=216,N=280,O=344,N-M=64=2^6

What is a concise way to describe this property? Thanks!